Combine milk, yeast and sugar in the bowl of a stand mixer fitted with a dough hook and whisk by hand.
Add the flour, eggs and yolks and salt and mix on low for about 6 minutes with the dough hook. Mix until you achieve a window pane. Start checking at 6 minutes. You may need more time, particularly if you use all-purpose flour.
Once the dough is strong, add the butter in chunks and beat until fully incorporating, Stopping the mixer periodically to push the butter down the sides of the bowl.
Leave the dough in mixer bowl and cover tightly with plastic wrap. Alternatively, remove dough to a shallow baking dish or ¼ sheet pan and wrap tightly with plastic. Refrigerate for at least 4 hours, or overnight. After this, you can freeze for 1 week. (You can let rise for 1-2 hours at room temp instead of chilling, but this dough is much easier to work with cold)
Shape and proof as directed for 1-2 hours, depending on the temp in your room.

Prepare the Fillings

Combine the sugar, cinnamon, and flour. Stir in the melted butter and water until evenly incorporated.
Stir the ricotta, pesto, and Parmesan together in a medium bowl until combined.

Fill and Shape the Babka

Line two 8x4 or 9x5 inch loaf pans with parchment so parchment is hanging over the long sides of the pans, but not the short sides. Like a sling.
Divide chilled brioche dough in half. Work one half at a time. Work quickly as dough will thaw fast and become difficult to work with.
Roll dough out on a lightly floured counter into a large rectangular shape. Dough should be about 1/8 inch thick.
Spread evenly with filling, leaving 1/2 inch at the long edge furthest from you clean. Tightly roll starting with the long edge closest to you. Pinch seam closed.
Cut this long dough snake in half, cross-wise. Cut each half in half length-wise. Twist each cut pair together. Then twist these two twists together. Tuck the ends under and carefully place in loaf pan.
Let rise until increased in size by about 50%. It will be very puffy.
About 30 minutes before loaf is proofed, preheat oven to 350℉.
Right before baking, egg wash all visible surfaces with an egg wash made with 1 large egg yolk and 1/2 large egg white and 2 tsp milk.
Bake for 30-40 minutes until a deep golden brown.

Babka Sweet & Savory v. 2

Churros