Step 1: Activate the Yeast
In a glass measuring cup, warm the milk to 105-115°F. Add 2 teaspoons of sugar and 4 teaspoons of yeast. Stir and let sit for 5-10 minutes until foamy. If it doesn't foam, start over – your yeast is dead.
Step 2: Make the Dough
In a stand mixer, combine the yeast mixture, ½ cup sugar, and ½ cup flour. Mix to combine. Add eggs, egg yolk, vanilla, and salt. Mix until incorporated. Add the remaining flour and use the dough hook to mix until a soft dough forms.
Step 3: Add the Butter
Add softened butter a little at a time, beating thoroughly after each addition. Knead for 4-5 minutes until dough is shiny, smooth, and elastic.
Step 4: First Rise
Lightly oil a large bowl, add the dough, cover with plastic wrap, and let rise in a warm place for 1½-2 hours, or until doubled in size.
Step 5: Prepare the Filling
Finely chop 5 ounces (½ bag) of chocolate. Keep the remaining chocolate whole.
Step 6: Shape the Babka
Punch down the dough and divide it in half. On a floured surface, roll one piece into an 18×10-inch rectangle.
Spread 2½ tbsp softened butter over the dough, leaving a ½-inch border. Brush the far long edge with egg wash.
Sprinkle half the chopped chocolate, half the whole chocolate pieces, and half the sugar over the butter.
Starting from the long side closest to you, roll the dough into a snug log. Pinch the seam to seal.
Bring the ends together to form a ring and pinch to seal. Twist the ring twice to form a double figure-8.
Gently place into a parchment-lined loaf pan.
Step 7: Second Rise
Cover with plastic wrap and let rise for 1½-2 hours, until the dough reaches the top of the pan.
Repeat steps 6-7 with the second half of the dough.
Step 8: Bake
Preheat oven to 350°F. Brush the tops with remaining egg wash. Bake for 40 minutes, until deep golden brown. The bottoms should sound hollow when tapped.
Step 9: Cool and Serve
Transfer to a wire rack and cool to room temperature before slicing.