Chocolate Babka

INGREDIENTS

• 3 1/4 cups all-purpose flour plus additional for dusting
• 2 whole large eggs
• 1/2 cup plus 2 teaspoons sugar
• 1 tablespoon heavy cream or whole milk
• 3/4 cup warm milk (105–115°F)
• 1 1/4 sticks (10 tablespoons) unsalted butter, cut into pieces and softened
• 1/4 cup sugar
• 3/4 teaspoon salt
• 1 teaspoon pure vanilla extract
• 3 teaspoons active dry yeast (from two 1/4-oz packages)
• 1 large egg yolk
• 5 tablespoons unsalted butter, well softened
• 2 (3 1/2- to 4-oz) bars fine-quality bittersweet chocolate (no more than 60% cacao if marked), finely chopped