Activate Yeast: In a stand mixer bowl, combine granulated sugar, active dry yeast, and warm milk. Allow the mixture to sit undisturbed for about 5 minutes, or until foamy.

Mix Dough: Add remaining ingredients (large egg, egg yolk, all-purpose flour, and salt) to the activated yeast mixture. Mix on low speed until a shaggy dough forms. Gradually incorporate unsalted butter, one tablespoon at a time.

Knead: Increase mixer speed to medium-high and knead dough for about 10 minutes until it feels smooth and elastic.

Chill Dough: Shape the dough into a ball, place it in an oiled bowl, cover with plastic wrap, and refrigerate for at least 8 hours.

Prepare Filling: Melt chocolate and unsalted butter together. Stir in cocoa powder, powdered sugar, and espresso powder until smooth.

Shape Dough: Roll chilled dough into a rectangle. Spread cooled chocolate filling evenly across, leaving a half-inch border.

Roll & Twist: Starting at the edge with filling, roll dough into a log. Cut log in half lengthwise and twist halves together, exposing filling.

Second Rise: Cover twisted babka and let it rise in a warm area for 1-2 hours, until puffy.

Bake: Preheat oven to 375°F. Bake for 25-30 minutes until golden brown and toothpick comes out clean.

Flavor Drizzle: Prepare syrup by boiling equal parts water and sugar with a dash of espresso. Brush warm syrup over baked babka.