Make the cream filling: In a saucepan, combine the egg yolks, granulated sugar, and vanilla sugar. Mix gently. Add the cornstarch and mix again. Gradually whisk in the hot milk. Cook over low heat, whisking constantly, until the mixture thickens. Pour the cream into a bowl, cover with plastic wrap directly on the surface, and refrigerate for at least 3 hours.

Make the dough: In a stand mixer, combine the flour, sugar, milk, yeast, egg, and salt. Knead on low speed for 3 to 5 minutes, until the dough is smooth.

Add the softened butter and knead on medium speed for 8 minutes.

Gather the dough into a ball in the center of the bowl, cover with a clean kitchen towel, and let rise for 2 hours in a warm place.

After 2 hours, punch down the dough and turn it out onto a floured work surface.

Divide the dough into 15 balls of about 1 3/4 ounces (50 grams) each. Place them on parchment paper, cover, and let rise for another hour.

For frying: Heat the oil. Fry the donuts on both sides until golden. Remove and drain on paper towels. Watch carefully, as they cook quickly.

Let the donuts cool, then cut them halfway through. Using a piping bag, fill them with the pastry cream and sprinkle with granulated sugar before serving.