For the Dough:
In a small saucepan or a bowl in the microwave, warm the milk until it’s lukewarm but not hot (about 110 degrees).
Add yeast and a pinch of sugar and let sit for 5 to 10 minutes, until slightly foamy.
In an electric mixer fitted with the dough hook, or in a food processor, mix together flour, 1/3 cup sugar, the salt, the vanilla, and the Buttery Sweet Dough Bakery Emulsion.
Beat or process in the yeast mixture and eggs until the dough comes together in a soft mass, about 2 minutes.
If the dough sticks to the side of the bowl and doesn’t come together, add a tablespoon more flour at a time until it does, beating very well in between additions.
Add half the butter and beat or pulse until the dough is smooth and elastic, 3 to 5 minutes, scraping down the sides of the bowl with a spatula as needed. Beat in the rest of the butter and continue to beat or pulse until the dough is smooth and stretchy, another 5 to 7 minutes.
Again, if the dough sticks to the sides of the bowl, add additional flour, 1 tablespoon at a time.
Butter a clean bowl, form the dough into a ball and roll it around in the bowl so all sides are buttered.
Cover the bowl with a clean towel and let it rise in a warm, draft-free place (inside of a turned-off oven with the oven light on is good) until it puffs and rises, about 1 to 2 hours. It may not double in bulk but it should rise.
Press the dough down with your hands, re-cover the bowl and refrigerate overnight (or, in a pinch, for at least 4 hours, but the flavor won’t be as developed).
For the Crumb Topping:
In a bowl, stir together flour, sugar, cookie mix, and salt.
Stir in melted butter until it is evenly distributed and forms large, moist crumbs.
Crumb topping can be prepared up to 3 days ahead and stored, covered, in the fridge.
For the Filling:
Mix together the melted butter and sugar cookie mix. Set aside until ready to roll out dough.
To Prepare the Babkas:
Butter two 9-inch loaf pans, then line with parchment paper, leaving 2 inches of paper hanging over on the sides to use as handles later.
Remove dough from refrigerator and divide in half.
On a floured surface, roll one piece into a 9-by-17-inch rectangle. Spread with half the filling (there’s no need to leave a border).
Sprinkle 1/4 cup sprinkles over the sugar cookie mix.
Starting with a long side, roll into a tight coil. Transfer the coil onto a dish towel or piece of plastic wrap and stick it in the freezer for 10 minutes. Repeat with the other piece of dough.
Slice one of the dough coils in half lengthwise to expose the filling.
Twist the halves together as if you were braiding them, then fold the braid in half so it’s about 9 inches long.
Place into a prepared pan, letting it curl around itself if it’s a little too long for the pan.
Cover loosely with a clean kitchen towel and let rise in a warm place for 1 to 1 1/2 hours, until puffy (it won’t quite double).
Alternatively, you can cover the pans with plastic wrap and let them rise in the refrigerator overnight; bring them back to room temperature for an hour before baking.
When you’re ready to bake, heat the oven to 350F.
Use your fingers to clump the crumb topping together and scatter all over the tops of the cakes.
Transfer to oven and bake until a tester goes into the cakes without any rubbery resistance and comes out clean, 40 to 50 minutes. The cakes will also sound hollow if you unmold them and tap on the bottom. An instant-read thermometer will read between 185 and 210 degrees.
As soon as the cakes come out of the oven, use a skewer or paring knife to pierce them all over going all the way to the bottom of the cakes.
Transfer to a wire rack to cool completely before serving.
For the Glaze:
Whisk all the ingredients together and drizzle over the two babkas.
If too thick add more milk. If too thin add more powdered sugar.
Top with sprinkles if desired.