FOR THE FILLING: Combine all ingredients in medium bowl; mix well. Set aside 1 Tbsp filling.
FOR THE TOPPING: Mix cinnamon & sugar together; mix well. Set aside.
FOR THE DOUGH: Adjust oven rack to middle position & heat oven to 200 degrees F. When oven reaches 200 degrees F., turn it off. Grease large bowl. Whisk milk, egg yolks & vanilla together in 1 C liquid measuring cup.
Using stand mixer fitted with dough hook, mix flour, sugar, yeast & salt on low speed until combined. Slowly add milk mixture & mix until dough comes together, about 3 minutes. Increase speed to medium low & add butter, 1 piece at a time, until incorporated, about 1 minute. Continue to mix until dough is smooth & comes away from sides of bowl, 10 - 12 minutes. Transfer dough to prepared bowl, cover with plastic wrap & place in turned off oven until dough has risen slightly, about 1 hour. Place in refrigerator until dough is firm & has doubled in size, at least 1 hour.
NOTE: Once you've added the butter in this step, if the dough is still sticking to the sides of the bowl after 5 minutes of mixing, add 2 - 4 Tbsp of extra flour.
Line 8 1/2 x 4 1/2" loaf pan with parchment paper, allowing excess to hang over edges. Punch down dough on lightly floured counter. Roll out dough to 20 x 14" rectangle. Spread all but 1 Tbsp reserved filling over dough, leaving 1/2" border around edges. Working from short side, roll dough into cylinder & pinch along seam to seal. Position cylinder seam side up & roll back & forth until stretched to 18" length. Spread reserved filling over top of cylinder. Fold cylinder on top of itself & pinch ends to seal. Gently twist double cylinder twice to form double figure eight. Place shaped dough seam side down in prepared pan, cover loosely with plastic & let rise in turned off oven until doubled in size, about 1 hour.
Lightly beat whole egg in bowl. Remove loaf pan from oven & discard plastic. Heat oven to 350 degrees F. Brush loaf with beaten egg & sprinkle with cinnamon/sugar mixture. Bake until deep golden brown & loaf registers 190 degrees, about 45 minutes. Let cool in pan on wire rack for 20 minutes. Remove loaf from pna & cool completely, about 2 hours. Serve.
NOTE: If you use a standard 9 x 5" loaf pan, start checking the babka for doneness after 40 minutes.
TO MAKE AHEAD: Instead of letting dough rise in step 4, cover shaped loaf with plastic wrap & refrigerate for up to 24 hours. Let dough sit at room temperature for 1 hour before baking.