Stir sugar, cinnamon, and a pinch of salt in a shallow bowl. Set aside.
Whisk flour, sugar, baking powder, baking soda, salt, and cinnamon in a large bowl.
In a measuring cup, whisk buttermilk, egg, melted butter, and vanilla until smooth.
Pour wet into dry. Stir with a spatula until a soft dough forms. Do not overmix; a few dry spots are fine.
Pour 1.5–2 inches of oil into a heavy pot or deep skillet. Heat to 350–360°F (175–182°C). Keep a thermometer clipped on if you have one.
Line a sheet pan with paper towels and set a wire rack on top if available.
No-cutter method (fastest): Scoop golf-ball portions, lightly roll, then press to 3/4-inch thick discs. Poke a hole with your finger and gently stretch.
Rolling method (prettiest): Lightly flour the counter. Pat or roll dough to 3/4-inch thick. Cut with a 3-inch cutter and a 1-inch cutter for holes.
Carefully lower 3–4 donuts into hot oil without crowding.
Fry 1 to 1 1/2 minutes per side until deep golden brown and cooked through.
Use a spider or tongs to transfer to the rack. Let excess oil drip for 20–30 seconds.
Toss warm donuts in the cinnamon sugar, coating all sides. If needed, lightly brush donuts with melted butter for extra adhesion.
Repeat with remaining dough, keeping the oil between 350–360°F. Adjust heat as needed.
