Heat the milk just above room temperature, then add sugar and dry yeast. Let it sit for 10 minutes until the yeast becomes active and a bit foamy.
In a bowl, whisk together two eggs, 1/4 cup of sugar, and tsp of vanilla paste.
Add flour, a pinch of salt, and softened butter. If using cold butter, add it after mixing all other ingredients.
Knead the dough on a floured surface for 15 minutes until smooth and elastic. If using a stand mixer with a dough hook, knead for 20 minutes. If the dough sticks to the edges, remove it with a spatula and sprinkle a little flour. Add a tablespoon of milk if the dough is too stiff.
Place the dough in a greased bowl, cover with plastic wrap, and let it rest in the refrigerator for 12 hours overnight.
Prepare the cherry sauce by simmering pitted cherries with 1/4 cup of sugar for 20-25 minutes until the water evaporates. Cool completely before using.
Whisk an egg with sugar and mix with cottage cheese. Adjust sweetness to taste.
Roll out the dough into a 12"x16" rectangle.
Spread the cheese mixture on the dough, then top with the cherry sauce.
Roll it up tightly from the long edge and refrigerate for 15 minutes before slicing.
Cut the roll in half, twist the halves, and shape into a babka loaf.
Place the loaf in a parchment-lined pan and let it rise for 2-2.5 hours. To speed up the process, you can leave it the oven preheated to 50°C/122°F.
When the dough has risen, preheat the oven to 375°F (190°C). Brush the babka with an egg wash from an egg yolk and 2/5 cup of milk.
Bake at 375°F (190°C) for 35-40 minutes, checking doneness with a skewer. Cover the loaf with foil or parchment paper if it browns too quickly on the outside.
While baking the babka, prepare a sugar syrup by boiling four tbsp water and 2/3 cup sugar. Brush the hot syrup over the loaf immediately after baking.
Cool your babka for 20 minutes in the pan, then transfer to a cooling rack to cool completely.
Slice, serve, and enjoy!