Peel and thinly slice the onions into rings or half-moons about 1/8" (3 mm) thick.

If using buttermilk, place the slices in a shallow bowl, pour the buttermilk over them, and let sit for 10–15 minutes.

In a wide bowl, whisk together flour, salt, pepper, and paprika.

Drain (but don’t rinse) the onions briefly and toss them in the seasoned flour until each piece is well coated.

Heat a large nonstick skillet over medium heat and add a thin layer of oil (1–2 tablespoons).

Add onions in a single layer as much as the pan allows without crowding and fry until they’re deep golden brown and crisp, about 6–10 minutes per batch.

Transfer fried onions to a paper-towel-lined tray to drain and lightly salt while still hot.

Repeat with remaining onions and allow to cool completely.

For a lower-oil finish, spread coated onions on a sheet and bake at 425°F (220°C) for 12–18 minutes, turning halfway.