Line a baking sheet with parchment paper. Preheat oven to 350°F.

In a small saucepan, heat cocoa powder, sugar, brown sugar, poppy seeds, milk, chocolate, cinnamon, and salt over low heat until combined and chocolate is melted. Continue cooking, stirring constantly, until the mixture has thickened.

Cool completely, covered, in the refrigerator. The filling can be made and stored, covered, in the refrigerator for up to 3 days.

Divide challah dough in half. Roll out dough to a ⅛-inch thick rectangle. Shmear half of filling over dough, leaving a 1-inch border. Roll dough, jelly-roll style, from short end. Pinch seam closed and place, seam side down, on lined baking sheet. Repeat with remaining dough.

Brush loaves with egg wash and bake at 350°F for 20 minutes. Rotate pans and continue baking for an additional 10 minutes. Cool on rack before serving.