Wake up the yeast: Mix warm milk, yeast, and a pinch of sugar in a bowl. Wait 5-10 minutes until foamy.
Make the dough: Add remaining sugar, melted butter, egg, egg yolk, salt, and half the flour. Mix until combined. Slowly add remaining flour. Knead for 8-10 minutes until smooth.
First rise: Put dough in a greased bowl and turn to coat. Cover and let rise in a warm place for 60-90 minutes until doubled.
Add chocolate and shape: Punch down dough and mix in chocolate chips. Divide into 12 equal pieces (about 75-80g each). Shape into balls and place in a greased 9x13-inch pan.
Second rise: Cover and let rise 30-45 minutes until puffy and touching. Heat oven to 350°F.
Egg wash and bake: Beat egg with 1 tablespoon milk. Brush on buns. Bake 20-25 minutes until golden brown.
Finish: Brush hot buns with melted butter. Cool in pan 10 minutes, then move to cooling rack.