For Coffee Cake:
In a medium bowl, sprinkle yeast and a pinch of granulated sugar over the warm milk. Let stand until foamy, about 5 minutes.
Whisk together the remaining ¼ cup plus 2 tablespoons granulated sugar, the whole egg and the egg yolk. Add to yeast mixture, combining gently.
In the bowl of your stand mixer, combine the flour and salt. Add the egg/yeast mixture and beat on low speed about 30 seconds.
Switch to the dough hook attachment. Add 1 stick butter and beat until smooth and soft, about 10 minutes (dough will be sticky).
Butter a large bowl or spray with vegetable oil.
Turn out dough onto floured surface; knead a few times until smooth. Place in the buttered bowl and cover with plastic wrap. Let stand in a warm place until doubled in volume, 1 to 1½ hours.
For the Filling:
Combine the chocolate, granulated sugar, and cinnamon.
Cut in butter with a pastry cutter or rub in with your fingers until combined.
Punch down dough. Transfer to a lightly floured work surface. Let the dough rest for 5 minutes.
Roll out the dough to an 18-inch square.
Brush the edges of the dough with egg wash. Spread filling over dough, reserving ½ cup for the topping.
Tightly roll dough like a jellyroll. Pinch seam to seal, and fold in half to bring ends together to form a U. Twist two or three times to “braid”.
Butter or oil a loaf pan or line with parchment paper.
Transfer dough to loaf pan and brush top with egg wash.
For Crumb Topping:
Combine the powdered sugar, flour, and butter with your fingers until crumbly.
Sprinkle crumb topping plus the reserved ½-cup chocolate filling over loaf.
Preheat oven to 350° F. Drape plastic wrap over dough. Let stand in a warm place until raised by half, 20 to 30 minutes.
Remove plastic wrap and bake, rotating loaf pan halfway through baking, until golden, about 1 hour.
Transfer loaf pan to a wire rack. Let cake cool completely before cutting.