Doughnuts

Add the remaining sugar, eggs, melted butter, salt, and half the flour. Mix with the paddle attachment until combined. Switch to the dough hook, add the remaining flour, and knead on medium speed for 5-7 minutes until the dough is smooth, elastic, and clears the sides of the bowl.

Place the dough in a greased bowl, cover, and let rise in a warm spot for 1 to 1.5 hours until doubled in volume.

Turn the dough out onto a floured surface and roll it to 1/2-inch thickness. Use a doughnut cutter (or two different-sized biscuit cutters) to cut out rings. Place the rings and holes on parchment squares. Cover loosely and proof for 30-45 minutes until very puffy.

Heat the vegetable oil in a heavy pot to 350°F (175°C). Carefully lower 2-3 doughnuts into the oil using the parchment squares. Fry for 1 to 1.5 minutes per side until golden brown. Drain on a wire rack set over paper towels.

Whisk the powdered sugar, milk, and vanilla together to make a smooth glaze. Dip the warm doughnuts completely into the glaze, let the excess drip off, and return to the wire rack to set.