Activate the yeast by combining it with warm milk and sugar, then let it sit for about 5-10 minutes until frothy.
In a separate bowl, whisk together the flour, melted butter, eggs, and vanilla extract.
Combine the frothy yeast mixture with the flour mixture, kneading until smooth.
Cover the dough and let it rise in a warm place until doubled in size, about 1-1.5 hours.
Once risen, punch down the dough and roll it out on a floured surface to about 1/2-inch thick.
Cut out the doughnuts using a round cutter, placing them on parchment-lined trays.
Cover the trays with a cloth and allow the doughnuts to rise again until puffy, about 30-45 minutes.
Heat oil in a deep fryer or large pot to 350°F (175°C).
Fry the doughnuts in batches, turning them until golden brown, about 2-3 minutes per side.
Drain the cooked doughnuts on a plate lined with paper towels.
While the doughnuts cool, whip the heavy cream with powdered sugar until soft peaks form.
Once cool, use a piping bag to fill the doughnuts with whipped cream.
Serve immediately or dust with additional powdered sugar before serving.