Peel and boil the potatoes until fork-tender.

Drain the potatoes and mash until completely smooth.

In another bowl, whisk together the flour, baking powder, sugar, and salt.

Add the mashed potatoes, milk, egg, and vanilla extract to the dry mixture. Stir until just combined.

Lightly flour your countertop and roll out the dough to about 1/2-inch thickness.

Use a donut cutter to cut out the shapes.

Heat vegetable oil in a frying pan or deep fryer to 350°F.

Carefully drop the donuts into the hot oil, frying until golden brown, about 2-3 minutes per side.

Remove the donuts and place them on a cooling rack.