While the dough is rising, heat 1 ½ cups heavy cream in a saucepan over medium heat until it starts to simmer.
In a separate bowl, whisk together ½ cup granulated sugar, 4 large egg yolks, and 2 tablespoons cornstarch until well combined.
Slowly pour the hot cream into the egg yolk mixture, whisking constantly.
Return the mixture to the saucepan and cook over medium heat, stirring constantly, until it thickens.
Remove the saucepan from the heat and stir in 1 teaspoon vanilla extract. Let the Bavarian cream cool to room temperature.
Once the dough has doubled in size, punch it down and roll it out on a floured surface to about ½-inch thickness.
Use a biscuit cutter or round cookie cutter to cut out circles from the dough.
Place the dough circles on a baking sheet and cover with a clean dish towel. Let them rise for about 30 minutes.
Heat vegetable oil in a deep fryer or a large pot to 350°F (175°C).
Carefully place a few dough circles in the hot oil and fry for about 2 minutes on each side or until golden brown.
Remove the fried donuts from the oil using a slotted spoon and drain them on a paper towel-lined plate.
Once the donuts have cooled, use a pastry bag or a plastic zip-top bag to fill them with the Bavarian cream filling.
Optional: Garnish the filled donuts with powdered sugar, drizzle them with chocolate ganache, or top them with whipped cream.