Roll your prepared and laminated sourdough croissant dough out to a rough rectangle measuring approximately 12.5 by 8.5 inches.
Using a sharp knife or pizza cutter, trim about 1/4 inch off each edge of the dough rectangle to create clean edges and expose the laminated layers. After trimming, your rectangle should measure roughly 12 by 8 inches.
Use a pastry brush to dust off any excess flour from the surface of the dough.
Cut the dough into strips about 3/4 inch thick. You should get approximately 10 strips from this amount of dough.
Take one candy cane and one strip of dough. Line up the end of the dough strip at the bottom of the candy cane at the straight end, not the hook.
Begin wrapping the dough around the candy cane, overlapping the dough slightly at the very beginning to create a seal.
Continue wrapping upward in a spiral motion, slightly overlapping each wrap with the previous one. As you wrap, gently press the dough down to help it adhere to itself.
If you are adding chocolate, after completing one full wrap around the candy cane, place a chocolate stick against the candy cane. Continue wrapping the dough around both the candy cane and the chocolate stick together. If you want chocolate in the top hook, break a chocolate stick in half and add to the short, straight part of the hook.
Work slowly and steadily when you reach the curved hook at the top. Be careful not to pull or tug too hard as this is where candy canes are most likely to break.
If your dough feels dry or is not sticking well, very lightly mist the surface with water using a spray bottle. Be extremely sparing with the water because too much will start dissolving the candy cane.
Repeat the wrapping process with the remaining candy canes and dough strips.
Place each wrapped candy cane seam side down on a parchment lined baking sheet, spacing them a few inches apart.
Lightly mist the tops of the wrapped candy canes with a fine spray of water.
Cover the baking sheet with plastic wrap or a lid.
Let them proof at room temperature for 6 to 12 hours. The exact time will vary based on your room temperature and humidity.
They are ready to bake when they look noticeably puffy and have increased in size by about 50 percent. You should be able to see the layers starting to separate from each other.
Preheat your oven to 400 degrees Fahrenheit.
Make your egg wash by whisking together the egg yolk, milk or cream, and vanilla extract in a small bowl.
Using a piece of paper towel or pastry brush, gently brush the egg wash over each proofed candy cane, being careful not to deflate them.
Take a piece of nonstick aluminum foil and fold it over itself 3 to 4 times to create a thicker, more stable piece. Tear or cut smaller pieces and loosely shape them around just the hook portion of each candy cane.
Place the baking sheet in the preheated oven and bake for 15 minutes with the foil in place.
After 15 minutes, carefully open the oven and remove the foil pieces from around the hooks. Close the oven and continue baking for another 3 to 7 minutes, for a total baking time of 18 to 22 minutes, until the candy canes are deep golden brown and the layers are fully separated and crispy.
Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack.