Place milk and yeast in a small bowl; stir to dissolve.
Place flour, salt, and eggs in the bowl of an electric mixer fitted with dough hook attachment; add yeast mixture and mix on low speed to combine and knead, about 5 minutes. Scrape down sides of bowl with a spatula; knead on medium speed until smooth and elastic, about 10 minutes.
In a large bowl, mix together butter and sugar. Add a few small pieces of butter mixture to dough; with the mixer on low, add remaining butter mixture, a little bit at a time. When all the butter mixture has been added, increase speed and continue mixing until smooth, shiny, comes away from the sides of the bowl, and is elastic, 6 to 10 minutes.
Butter a large bowl, transfer dough to prepared bowl, and cover with plastic wrap; let stand in a warm place until doubled in volume, about 2 hours.
Lift dough from bowl and drop back into bowl to deflate; repeat process once or twice. Cover bowl and transfer to refrigerator to chill for at least 8 hours and up to overnight.
Butter 20 5-ounce baba molds and place on a baking sheet. Divide dough into 20 equal pieces; pinch each piece of dough to form balls. Place each ball of dough into prepared molds.
In a small bowl, whisk together egg yolk and milk. Brush dough with egg yolk mixture, reserving remaining. Spray a piece of plastic wrap with nonstick cooking spray; cover dough, cooking spray-side down, and let stand in a warm place until doubled in volume, 1 to 1 1/2 hours.
Preheat oven to 400 degrees in a convection oven (425 degrees in a conventional oven).
Working from the outside inward, brush each baba very lightly with reserved egg yolk mixture. Transfer molds to oven and bake until baba just begins to turn golden, about 5 minutes. Reduce temperature to 375 degrees (if using a convection oven; 400 if using a conventional oven) and continue baking until deep golden-brown and internal temperature reaches 205 degrees on an instant-read thermometer, 5 to 10 minutes more.
Remove from oven and let cool in mold for 5 minutes. Unmold onto a wire rack and let cool completely. Poke bases of babas all over with a toothpick. Working in batches, gently drop babas into hot rum syrup, submerging completely; let soak until there are no more bubbles. Place on a rack set over a rimmed baking sheet. Repeat process with remaining baba; serve drizzled with additional rum syrup, whipped cream, and cherries, if desired.