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Shaping the doughnuts : Once the dough has risen, flatten it to release any air bubbles. Roll out to about 1/2-inch thickness on a floured surface. Use a round cookie cutter (about 3 inches in diameter) to cut out circles. Re-roll scraps if necessary.
Second Rise : Place the cut doughnuts on a parchment-lined baking sheet, cover, and let rise for another 30 to 45 minutes, or until puffed and slightly risen.
To Fry the Donuts : Heat vegetable oil in a deep fryer or large saucepan to 350°F (175°C). Fry 2 or 3 donuts at a time for about 1 to 2 minutes per side, or until golden brown. Use a slotted spoon to remove and drain on a paper towel-lined plate.
For the vanilla custard filling
Heat the milk : In a medium saucepan, heat the milk over medium heat until it begins to simmer. Do not let it boil.
Fouetter les jaunes d’oeufs et le sucre: In a separate bowl, whisk together the egg yolks , sugar and cornstarch until smooth and pale.
Tempering the egg mixture : Slowly pour half of the hot milk into the egg mixture, whisking constantly to prevent curdling. Pour the tempered egg mixture back into the saucepan with the remaining milk.
Cook the custard : Cook over medium-low heat, stirring constantly, until the mixture thickens and coats the back of a spoon, about 2 to 3 minutes. Remove from heat and stir in the vanilla extract and butter.
Chill the custard : Transfer the custard to a bowl, cover with plastic wrap (pressing it directly onto the surface to prevent a skin from forming), and refrigerate until completely chilled and set.
Fill and assemble the donuts
Prepare the custard : Once the custard has cooled, transfer it to a piping bag fitted with a small round nozzle.
Fill the donuts : Using a skewer or the back of a spoon, poke a small hole in the side of each cooled donut. Insert the piping bag and fill each donut with pastry cream until slightly full.
Enrober les beignets: Roll the filled donuts in powdered sugar or cinnamon sugar, or dip the tops in melted chocolate frosting if desired.
