1 package active dry yeast (2½ teaspoons)
⅔ cup (160 grams) milk, at room temperature
3½ cups (490 grams) unbleached all-purpose flour
1½ cups sugar, divided
2 teaspoons kosher salt
7 tablespoons butter, at room temperature, cut into 6 or 8 pieces
Canola oil, for frying
vanilla cream filling
6 tablespoons heavy cream
1 recipe Pastry Cream, chilled
In a stand mixer fitted with the dough hook, combine the yeast and milk. Stir together briefly, then let sit for about 1 minute to dissolve the yeast. Add the flour, ⅓ cup(70 grams) of the sugar, salt, and eggs and mix on low speed for about 1 minute, or until the dough comes together. Then, still on low speed, mix for another 2 to 3 minutes to develop the dough further. Now, begin to add the butter, a few pieces at a time, and continue to mix for 5 to 6 minutes, or until the butter is fully incorporated and the dough is soft and cohesive.
Remove the dough from the bowl, wrap tightly in plastic wrap, and refrigerate for at least 6 hours, or up to 15 hours.
Lightly flour a baking sheet. On a well-floured work surface, roll out the dough into a 12-inch square about ½-inch thick. Using a 3½- to 4-inch round biscuit cutter, cut out 9 doughnuts. Arrange them on the prepared baking sheet, cover with plastic wrap, and place in a warm spot to rise for 2 to 3 hours, or until they are about doubled in height and feel poufy and pillowy.
When ready to fry, line a baking sheet with paper towels. Pour oil to a depth of about 3 inches into a large, heavy saucepan and heat over medium-high heat until hot. To test the oil, throw in a pinch of flour. If it sizzles on contact, the oil is ready. (It should be 350ºF if you are using a thermometer.) Working in batches, place the doughnuts in the hot oil, being careful not to crowd them. Fry on the first side for 2 to 3 minutes, or until brown. Then gently flip them and fry for another 2 to 3 minutes, or until brown on the second side. Using a slotted spoon, transfer the doughnuts to the prepared tray and let cool for a few minutes, or until cool enough to handle.
Place the remaining 1 cup sugar in a small bowl. One at a time, toss the warm doughnuts in the sugar to coat evenly. As each doughnut is coated, return it to the tray to cool completely. This will take 30 to 40 minutes.
To make the vanilla cream filling:
While the doughnuts are cooling, whip the heavy cream until it holds stiff peaks. Using a rubber spatula, fold it into the pastry cream. You should have about 3 cups.
When the doughnuts are completely cooled, poke a hole in the side of each one, spacing it equidistant between the top and bottom. Fit a pastry bag with a small round tip and fill the bag with the filling. Squirt about ⅓ cup filling into each doughnut. Serve immediately.