3-1/2 cups flour (840 milliliters), plus more if needed
1 egg yolk
2/3 cup (160 milliliters) butter, room temperature, cubed
1/3 cup (80 milliliters) icing sugar
1 cup (240 milliliters) ricotta
1/2 cup (120 milliliters) melted dark chocolate chips
2/3 cup (160 milliliters) butter, room temperature
1-1/2 cups (360 milliliters) sugar
1 cup (240 milliliters) water
1 teaspoon (5 milliliters) vanilla extract
Add milk, sugar, and yeast to the bowl of a stand mixer and mix together. Let sit five minutes.
Start stand mixer with dough attachment and mix in one cup flour on low. Add eggs and egg yolk and continue mixing. Slowly add remaining flour while mixing. Turn mixer to medium and add butter cubes one at a time. Continue mixing for 10-15 minutes, or until dough is soft, sticky, and shiny.
Grease a bowl with butter. Take dough out of stand mixer and add to greased bowl. Cover bowl with a tea towel or plastic wrap. Let dough rest two hours.
Mix together icing sugar and ricotta. Slowly add melted chocolate.
Mix in butter. Set aside.
Preheat oven to 350 F (175 C).
Turn dough out onto a lightly floured counter. Roll out into a large rectangle. Spread filling onto rectangle, leaving a border. Starting at one of the long edges, roll rectangle up tightly to form a log. When you get near the end, apply a bit of water along the remaining border of the dough to help seal it closed when you finish rolling it up. Trim the ends. Using a sharp knife, cut the log down the middle lengthwise. With cut ends facing up, place strips of dough side by side, then fold one strip over the other, then fold that strip over the first strip, and continue until you create a braid of sorts. Carefully place the dough into a large greased loaf pan. Bake babka for 40-50 minutes.
Melt sugar in water on the stove. Let boil five to ten minutes until mixture starts to thicken. Take off the heat and stir in vanilla extract. Set aside.
As soon as you remove the babka from the oven, pour simple syrup evenly over the top of the loaf. Let cool slightly before removing from pan.