Bloom the yeast first. Combine the warm milk and warm water in a small bowl or measuring cup. Both should be between 110 and 115 degrees F. Stir in the 5 grams of honey and the yeast until no dry granules remain. Let sit undisturbed for 10 minutes. A properly bloomed yeast mixture will be noticeably foamy and smell yeasty and slightly sweet. If nothing happens after 10 minutes your yeast is dead or your liquid was too hot. Discard and start fresh before continuing.
Warm the Greek yogurt in the microwave for about 30 seconds, just enough to take the chill off. You want it slightly warm but not hot.
In a large bowl whisk together the white whole wheat flour, bread flour, and salt. In a separate bowl whisk together the bloomed yeast mixture, warmed yogurt, remaining 35 grams of honey, and egg until smooth, then mix in the softened butter until fully incorporated. Pour the wet mixture into the dry ingredients and mix until a soft slightly tacky dough forms.
Cover the bowl and let the dough rest for 30 minutes. This rest is important because the Greek yogurt hydrates the flour more slowly than water does. The dough will feel stickier in the first few minutes but becomes significantly more cohesive and workable after the rest without adding extra flour.
After the rest, knead the dough in a stand mixer on speed 2 for 6 to 8 minutes or by hand for 8 to 10 minutes until it smooths out and becomes elastic. You are looking for a partial windowpane where the dough stretches without immediately tearing. If the dough is still unworkably wet after the rest, add bread flour 10 grams at a time, mixing fully between each addition before deciding if more is needed.
Place the dough in a lightly oiled bowl, cover tightly, and let it bulk rise at room temperature until doubled in size. Yeasted dough rises significantly faster than sourdough so check it early. Expect 1 to 1.5 hours depending on your kitchen temperature. The dough should feel airy and jiggly when you gently shake the bowl.
Turn the dough out onto a lightly floured surface. Pat the dough into a rectangle approximately 14 inches tall by 10 inches wide, with the 14 inch side closest to you. Fold the left side of the 10 inch width in toward the center, then fold the right side in toward the center. Starting from the edge closest to you begin rolling the dough upward away from you, tugging gently as you go to build surface tension with each revolution. Once you have rolled it over the seam, pinch the sides together firmly and place seam side down in a parchment lined or lightly greased 9x5 loaf pan, pressing gently so the log touches both short ends of the pan.
Cover the shaped loaf tightly and let it proof at room temperature for 45 minutes to 1 hour until the dough crowns about 1 inch above the rim of the pan. Use the poke test to confirm readiness. Lightly oil your finger and press about half an inch into the dough. If it springs back slowly and leaves a slight indent it is ready to bake. If it springs back immediately it needs more time. If the indent stays completely without springing back at all, get it in the oven immediately.
Preheat the oven to 375 degrees F.
Whisk together the egg and splash of whole milk for the egg wash and brush the top of the loaf gently with one thin even coat. Place a second loaf pan of the same size inverted loosely over the top of your loaf pan before placing it in the oven. This controls the oven spring during the first 10 minutes of baking and prevents side splitting by keeping moisture around the loaf so the top stays pliable long enough for the spring to go upward rather than outward.
Bake for 38-42 minutes. Optional, bake for 10 minutes with the inverted pan on top, then carefully remove it and continue baking for 28 to 32 more minutes until deep golden brown. Honey deepens the crust color faster than sugar so keep an eye on it and tent loosely with foil if the top is browning too fast before the interior is done. The loaf is done when an instant read thermometer inserted in the center reads 190 to 195 degrees F.
Remove from the oven and brush immediately with melted butter. Let the loaf cool in the pan for 10 minutes, then transfer to a wire rack. Cool for at least 2 hours before slicing. This is an enriched loaf and cutting too early will give you a gummy crumb regardless of how well it baked.