Lightly spray two 8 1/2 to 9-inch loaf pans with non-stick cooking spray. Line the pans with parchment paper, cutting the parchment to fit with an overhang on all sides of the pan. Lightly spray the parchment paper with nonstick cooking spray.
MAKE THE DOUGH:
In the bowl of a stand mixer whisk together the flour, sugar, yeast, and salt, and then attach the dough hook.
In a large measuring cup whisk together the eggs, egg yolk, milk, and vanilla.
Turn the mixer on low and slowly pour in the egg mixture, scraping down the sides of the bowl as needed.
With the mixer still running, add in a few cubes of the butter at a time and mix until combined. Increase the speed to medium and knead the dough for 10 minutes, or until the dough is smooth and it pulls away from the sides of the bowl.
Lightly spray a large bowl with nonstick cooking spray and place the dough into the bowl. Cover the bowl with plastic wrap and let the dough rise in a warm place until doubled in size, about 80-100 minutes.
MAKE THE CHOCOLATE FILLING:
While the dough rises, make the chocolate filling by setting a medium heatproof bowl over a saucepan with 2 inches of swimming water. Add the chocolate and butter to the bowl and stir often until the chocolate is melted.
Let the melted chocolate sit at room temperature for 15 minutes, and then stir in the corn syrup followed by the ground cookie wafers.
SHAPE THE BABKA BREAD:
Working with half of the dough at a time, roll half of the dough out into a floured surface into a 10x14-inch rectangle.
Evenly spread half of the chocolate filling over the dough. Starting with the 10-inch side, roll the dough tightly like you’re rolling cinnamon rolls. Place the roll seam side down onto a baking sheet lined with wax paper. Repeat with the remaining dough and chocolate filling. Freeze the rolls on the baking sheet for 20 minutes.
Remove the rolls from the freezer. Working with 1 roll at a time, use a sharp kitchen knife to cut the roll in half lengthwise down the center. Twist each piece of roll, and then twist the two pieces together; over, under, over, under, all the ways down the roll. Pinch the ends of the roll in place and place it into one of the prepared loaf pans. Repeat with the second roll. Cover the pans with greased plastic wrap and let the dough rise at room temperature until nearly doubled, about 90-120 minutes. During the last 20 minutes of rising, move the oven rack to the middle position and preheat the oven to 350 degrees F.
BAKE THE BABKA:
Once the babka is done rising, place the pans in the oven and bake until the internal temperature reaches 190 degrees F, about 40-50 minutes. Remove the bread from the oven and place them on a wire rack.
MAKE THE SUGAR SYRUP:
While the babka bakes, make the sugar syrup by whisking together the sugar and water in a small saucepan. Set the saucepan over medium heat and bring it to a boil. Let the sugar water boil for 2 minutes, and then remove it from the heat.
POKE THE BAKED BABKA:
Poke each break 40 times with a wooden skewer. Pour half of the sugar syrup over one babka, and then pour the rest of the syrup over the other. Let the babka cool in the pan for 40 minutes, and then use the parchment overhang to lift the babka from the pans. Let the babka cool completely on the wire rack.
MAKE THE CHOCOLATE GLAZE:
Make the chocolate glaze by setting a medium heatproof bowl over a saucepan with 2 inches of swimming water. Add the chocolate and butter to the bowl and stir often until the chocolate is melted and smooth. Stir in the corn syrup.
Spread the glaze over the tops of the babka breads and let the chocolate set for about 30 minutes before slicing and serving.