Set up for success. Line a baking sheet with parchment and dust lightly with flour. Set a wire rack over another sheet for draining after frying. Mix the cinnamon sugar in a shallow bowl and set aside.
Mix dry ingredients. In a medium bowl, whisk cake flour, baking powder, baking soda, salt, and nutmeg until well combined.
Whisk wet ingredients. In a large bowl, whisk sugar, melted butter, egg, and vanilla until smooth. Add sour cream and buttermilk and whisk until creamy.
Bring the dough together. Add dry ingredients to the wet and fold with a spatula just until no dry pockets remain. The dough will be soft and slightly sticky. Avoid overmixing.
Rest and chill. Turn dough onto the prepared parchment. Dust lightly with flour, pat into a 3/4-inch-thick slab, and cover with plastic. Chill 30–45 minutes to firm up for easier cutting.
Cut the doughnuts. Dust the top with flour and use a 3-inch doughnut cutter (or two round cutters, 3-inch and 1-inch) to cut as many doughnuts as possible. Transfer to the parchment-lined sheet. Gently press scraps together, pat, and cut again once more. Avoid over-handling.
Heat the oil. Pour oil into a heavy pot or Dutch oven to a depth of 2–3 inches. Heat to 340°F (171°C). Keep a thermometer clipped to the side for accuracy.
First fry for structure. Fry 2–3 doughnuts at a time, about 1–1 1/2 minutes per side, keeping the oil between 335–345°F. They should puff and develop slight cracks. Remove to the wire rack to rest 1 minute.
Second fry for crisp ridges. Increase oil to 360°F (182°C). Return doughnuts to the oil for 30–45 seconds per side until deep golden with craggy edges. Drain on the rack.
Coat while warm. When the doughnuts are cool enough to handle but still warm, toss generously in cinnamon sugar. Coat doughnut holes too—cook them about 1 minute total, turning often.
Serve. Enjoy right away for the best texture. They’re fantastic with coffee or hot chocolate.
