Add the flour, baking powder, baking soda, salt, cinnamon, and nutmeg to a bowl. Whisk them well so the spices and leaveners spread evenly. Set the bowl aside while you make the wet mix.
Beat the eggs until they look very bubbly and a bit frothy. Then add the sugar and mix until combined. This step adds air, which helps the donuts turn out light.
Stir the sour cream and vanilla into the egg mixture. Mix until smooth and creamy with no streaks. The sour cream is what makes these donuts so soft and moist.
With the mixer running on low, slowly add the dry ingredients. Stop before everything is fully mixed. Fold in the rest by hand with a spatula, and expect a wet, sticky dough.
Scoop the dough onto plastic wrap and shape it into a flat disc. Wrap it tightly and refrigerate for at least 1 hour. Chilling makes the sticky dough much easier to roll and cut.
Dust your counter generously with flour and place the chilled dough on top. Flour the top of the dough, then roll it into a square about 10 by 10 inches. Keep adding flour underneath as you roll so nothing sticks.
Dip your donut cutter in flour before every cut. Press straight down, then lift out the donuts and the little holes. Gather the scraps, reroll them, and cut again until the dough is used up.
Pour 1 to 2 inches of oil into a deep pot or fryer. Heat it to 375°F and check it with a thermometer. Steady heat is the secret to fluffy, non-greasy donuts.
Fry a few donuts at a time, so the pot never gets crowded. Cook them for about 2 minutes per side until deep golden brown. Move them to a baking rack, and reheat the oil to 375°F between batches.
Mix the sugar and cinnamon in a shallow bowl. While the donuts are still warm, press each one into the mixture and flip to coat both sides. Serve them right away for the best texture