Mix 35g hot espresso 35g water and 25 to 30g Dutch processed cocoa powder in a bowl. Cover and let bloom for 1 hour.

In the bowl of a stand mixer combine bloomed chocolate mixture 60g active sourdough starter 30g water 60g milk 40g sugar 25g softened butter 5g salt 2g vanilla extract 2g peppermint extract and 30 to 35g egg white. Mix briefly to combine.

Add 300g bread flour. Mix with dough hook on low speed until a shaggy dough forms.

Cover bowl and let rest at room temperature for 30 minutes.

Perform a stretch and fold. Grab one side of the dough stretch it up and fold it over to the opposite side. Rotate bowl 90 degrees and repeat. Do this 4 times total going around the bowl. Cover and rest 30 minutes.

Perform a second stretch and fold using the same technique. Cover and rest 30 minutes.

Shape dough into a smooth ball and place in a lightly greased container or bowl. Cover tightly and refrigerate overnight or 8 to 12 hours.

Pull out about 21 inches (53 cm) of parchment paper. Create a 7 inch (18 cm) square template by folding. Place ruler in middle fold left edge to 7 inch (18 cm) mark and crease. Flip ruler line up 7 inch (18 cm) mark with creased edge fold right edge over and crease. Rotate 90 degrees and repeat for other two sides.

Cut 227g (2 sticks) butter into 3 to 4 slices. Place in center of parchment template. Fold parchment over butter and gently roll to fill entire 7 inch (18 cm) square evenly. Leave at room temperature in parchment while preparing dough.

Remove dough from refrigerator. On lightly floured surface roll dough to 10 inch (25 cm) square.

Remove butter block from parchment. Check temperature butter should be cold and firm but pliable. If too soft refrigerate 5 minutes.

Place 7 inch (18 cm) butter block in center of 10 inch (25 cm) dough square positioned like a diamond rotated 45 degrees.

Fold each corner of dough to meet in center completely encasing butter. Pinch seams closed.

Using toothpick or skewer poke holes through top and bottom edges to release trapped air.

Gently roll dough to 17.5 to 18 inches (44 to 46 cm) long by 10 inches (25 cm) wide. Trim short ends.

Fold bottom edge up 2 inches (5 cm). Fold top edge down to meet bottom folded edge. Fold entire piece in half like closing a book.

Wrap well and refrigerate 1 hour.

Remove from refrigerator and rest 5 minutes. Check butter temperature by gently pressing dough. Butter should be cold but pliable.

Roll dough to 21.5 inches (55 cm) long by 5 to 6 inches (13 to 15 cm) wide. Trim short edges to 21 inches (53 cm) long.

Fold into thirds like a letter. Fold bottom edge up two thirds of the way. Fold top piece all the way down to meet bottom folded edge.

Wrap well and refrigerate 1 hour to up to 18 hours.

Remove dough from refrigerator and rest 5 to 10 minutes. Check butter temperature should be easily manipulated but not too soft.

Roll dough to slightly larger than 12 inches (30 cm) by 9 inches (23 cm). Trim edges about one quarter inch (0.6 cm) on each side to create clean rectangle of exactly 12 inches (30 cm) by 9 inches (23 cm).

Lift dough slightly and allow to naturally shrink back. Cover with plastic wrap and rest in refrigerator 15 to 20 minutes.

With 9 inch (23 cm) side parallel to you make marks at 3 inches (7.5 cm) and 6 inches (15 cm) along width at top and bottom edges. Connect marks with ruler and sharp knife cutting straight up and down no dragging. You now have three 3 inch (7.5 cm) by 12 inch (30 cm) rectangles.

Match top corner of each rectangle with opposite bottom corner to create triangle. Cut along diagonal using up and down motion. You will get 2 triangles per rectangle for 6 croissants total.

Gently stretch each triangle 1 to 2 inches (2.5 to 5 cm) longer. Starting from wide base roll toward point. First 2 to 3 rolls should be firm then continue with snug tension.

When 1 to 1.5 inches (2.5 to 4 cm) from tip press tail firmly against work surface. Roll croissant body on top of pressed tail.

Place shaped croissants on parchment lined baking sheets tail tucked underneath. Space at least 3 inches (7.5 cm) apart.

Preheat oven to 400 degrees F 200 degrees C.

Bake 20 to 25 minutes until croissants feel light when lifted bottoms sound hollow when tapped and internal temperature reaches 200 to 205 degrees F 93 to 96 degrees C.

Let sit on baking sheet 10 minutes then transfer to wire rack. Cool at least 30 to 45 minutes before cutting.

In medium saucepan combine 240g milk 60g heavy cream and 25g sugar half the total sugar. Heat over medium until steaming with small bubbles around edges. Remove from heat.

Whisk together 3 egg yolks remaining 25g sugar 20g cornstarch and pinch of salt until smooth pale yellow and slightly thickened.

Slowly pour one third hot milk mixture into egg yolk mixture whisking constantly to temper.

Pour tempered mixture back into saucepan with remaining hot milk. Whisk thoroughly.

Return to medium heat. Cook whisking constantly until mixture thickens and comes to full boil about 3 to 5 minutes.

Continue whisking vigorously for 1 full minute after boil.

Remove from heat. Add 30g cold butter cubes and whisk until melted and incorporated.

Stir in 1 teaspoon 5g vanilla extract and one quarter teaspoon 1.25g peppermint extract. Taste and add more peppermint if desired.

Strain custard through fine mesh sieve into clean bowl.

Press plastic wrap directly onto surface. Refrigerate at least 2 hours or overnight until completely cold.

Whisk chilled custard smooth. Transfer to piping bag with medium round tip.

For bottom injection poke 2 to 3 small holes in bottom of each croissant. Insert tip and squeeze custard throughout about one quarter cup 60ml per croissant.

For split and fill slice croissants horizontally. Pipe custard on bottom half and replace top.