Warm the milk to about 90°F, warm to the touch but not hot. Pour it into a large bowl, add the yeast, stir gently, and let sit until foamy, about 5 minutes.
Add the eggs, melted butter, sugar, and salt to the yeast mixture. Using a stand mixer fitted with a dough hook or an electric mixer, mix until combined. Add about half of the flour, 2 cups plus 2 tablespoons, and mix until smooth. Add the remaining flour and continue mixing until the dough pulls away from the sides of the bowl and forms a soft, cohesive dough. If the dough feels very wet or sticky, add additional flour 2 tablespoons at a time just until manageable.
If the dough becomes too thick for the mixer, transfer it to a lightly floured surface and knead gently until smooth and elastic. Lightly oil a large bowl, place the dough inside, turn once to coat, and cover. Let rise at room temperature until doubled in size, about 1 hour.
Turn the dough out onto a well-floured surface and roll it to about ½-inch thickness. Cut into doughnuts using a doughnut cutter, into any shape you desire, I used a 3 inch heart cookie cutter. Gather any lefotver scraps gently, knead just until smooth, let rest for a few minutes, then re-roll and cut again.
Arrange the doughnuts on floured baking sheets with plenty of space between them. Cover loosely with a kitchen towel and let rise until slightly puffed and delicate, about 45 minutes. If your kitchen is cool, heat the oven to 200°F, turn it off, place the baking sheets inside, and leave the door slightly ajar.
About 15 minutes before the doughnuts are ready, heat the oil in a heavy-bottomed pot or Dutch oven to 375°F. Line cooling racks or baking sheets with paper towels.
Fry the doughnuts a few at a time, carefully lowering them into the oil. If they are very soft, use a metal spatula to slide them in. Fry until the bottoms are deep golden, about 45 seconds to 1 minute, then flip and fry until golden all over. Doughnut holes will cook more quickly.
Transfer the fried doughnuts to the prepared racks and continue frying the remaining dough, adjusting the heat as needed to keep the oil at 375°F.Once all of the doughnuts are fried and still slightly warm, fill them with the brownie batter pastry cream. Use a piping bag fitted with a filling tip to pipe the cream into the side of each doughnut. If you do not have a filling tip, use the handle of a wooden spoon or a small dowel to gently create a channel in the side of the doughnut, then pipe the cream into the opening.Dip the filled doughnuts into the chocolate glaze, allowing any excess to drip off. Immediately sprinkle with sprinkles before the glaze sets.