In a small bowl, sprinkle the yeast over the warm milk. Stir to combine and let sit until frothy, about 10 minutes.
In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, sugar, and salt. Slowly mix in the frothy yeast with the milk, followed by the egg, butter, and vanilla extract to form a smooth dough.
If the dough is still too crumbly, slowly add a little more lukewarm milk.
On a lightly floured surface, knead the dough until smooth and elastic, then knead in the chopped chocolate until evenly distributed.
Transfer to a large bowl, cover with plastic or a towel, and allow to rise until doubled, 1-2 hours.
Line two baking sheets with parchment or lightly grease.
Once doubled, place the dough on a lightly floured surface and divide into 8 equal rolls.
Form each roll into a smooth oval, tucking the seams under, and place on the prepared baking sheets. Cover with a towel and allow to rest at room temperature for 30 minutes or until puffed.
Preheat oven to 350˚F (180˚C).
In a small bowl, beat together the egg yolk and 1 tablespoon (15 milliliters) milk.
Brush the top and sides of each piece of puffed dough with the egg wash.
Use sharp scissors to cut three to four 1/2 inch (1.25 centimeter) deep triangles lengthwise along the top of each oval.
Bake the buns in the preheated oven until golden brown, 15-20 minutes.
Remove to a wire rack to cool slightly. These Schoggiweggli are best warm from the oven and within a day.