Place the yeast and half a teaspoon sugar in a small bowl. Add the lukewarm water and stir gently to mix. Set aside until foamy, five to ten minutes.

In a stand mixer fitted with a dough hook, mix together the flour, remaining sugar, and vanilla.

In a medium saucepan, scald the milk (bring almost to a boil, until milk is just simmering). Allow to sit for one minute to cool just slightly.

With mixer on low, add the water-yeast mixture, milk, and melted butter. Add eggs one at a time.

When the dough begins to come together, after two to three minutes, turn off mixer and scrape down the sides. Raise the speed to high and mix for another five to ten minutes until the dough is shiny and elastic.

Place dough in a greased bowl with a damp towel on top. Allow to rise until it has doubled, about one to two hours.

While dough is rising, make the filling and the topping.

Beat the softened cream cheese, powdered sugar, vanilla, baking powder, and salt. Fold in the sprinkles.

Combine the sugars in a small bowl. Stir in the melted butter and the flour. Add the sprinkles and combine using fingers.

Prepare three 8 - and- 1/2- x 4 - and- 1/2-inch greased loaf pans.

Cut the dough into three equal parts (use a food scale for precision). Roll out one part into a rectangle. Spread with one- third of the cream cheese filling and roll up along the shorter side (to create more swirls inside). 

Once the dough is formed into a swirled log, cut it straight down the middle so the filling is exposed. Cut half an inch off each end. Layer each cut piece on top of one another and twist. Place in a greased loaf pan.

Repeat with other two pieces of babka dough. Lightly drape a kitchen towel over the top of pans. Allow to rise another 30 minutes. Preheat oven to 350 degrees while the dough rises.

Before baking, add one-third of the crumb topping on each babka. Bake for 30–35 minutes. The edges should be slightly brown and the middle should be slightly doughy.

Allow to cool for five to 10 minutes. Using a butter knife, loosen sides of the babkas from the pans and place on top of parchment wire rack to cool. Place babkas on a platter.

Combine confectioners’ sugar, milk, and salt in a bowl. Drizzle on top of each babka.