Heat milk in a small saucepan until warm (about 100 degrees F. Too warm or too cool, and the yeast won't activate). Transfer to a large bowl and whisk in yeast and one tablespoon sugar; let sit until foamy, 5–10 minutes.

Whisk in egg yolks, vanilla, and ½ cup butter. Add remaining sugar, salt, and 3 cups flour; mix until a shaggy dough forms. If the dough is dry, add a bit more milk, if it's sticky, add a bit more flour. Knead dough on a lightly floured surface or in an electric mixer with a dough hook attachment until supple, smooth, and no longer shiny, 5–10 minutes.

Transfer to a large buttered bowl. Cover and let sit in a warm place until doubled in size, about 1½–2½ hours.

When ready to assemble, mix chocolate, brown sugar, and cinnamon in a small bowl.

Turn out dough onto a lightly floured surface; divide into three portions. Shape each into a 12”-long rope. Roll out each rope to a 12x6” rectangle about ⅛” thick. Brush with butter and top with chocolate mixture, pressing gently. Don't be afraid to use all the chocolate! Roll up carefully making sure to not let in any air bubbles or let the filling fall out. Form a log; pinch seam to seal.

Place logs, seam side down, side by side on a parchment-lined baking sheet. Pinch logs together at one end; braid, then pinch ends together and tuck under. Cover loosely and let sit in a warm place until 1½ times larger, 1–2 hours.

Preheat oven to 350 degrees F. Beat egg yolk with 1 tablespoon water in a small bowl. Brush dough with egg wash; sprinkle generously with granulated sugar. Bake until top is golden brown and babkallah sounds hollow when bottom is tapped, about 35–45 minutes. Let cool on a wire rack. Eat!