Peel the onions and slice into 1/2-inch thick rings. Gently separate the rings and discard the small center pieces that won't hold together. Place rings on a tray and refrigerate while you prepare batter to help them firm up (10–15 minutes).

Make batter

In a large bowl, whisk together the all-purpose flour, cornstarch, baking powder, kosher salt, black pepper, and smoked paprika if using. In a separate small bowl, lightly beat the egg and whisk with the cold club soda (or cold beer). Pour the wet mixture into the dry ingredients and stir until just combined; a few small lumps are okay. Batter should be thick enough to coat but still pourable; if too thick add up to 2 tablespoons more cold club soda.

Heat oil

Pour neutral frying oil into a large, deep pot or Dutch oven to a depth of about 3 inches (roughly 1 liter). Heat the oil to 350°F (175°C) using a candy or instant-read thermometer. If you don't have a thermometer, heat oil until a small drop of batter sizzles and rises to the surface steadily.

Coat and fry

Working in batches to avoid overcrowding (4–6 rings per batch depending on pot size), dust onion rings lightly with a tablespoon of flour (this helps batter adhere). Dip rings into the batter, letting excess drip off, then carefully lower into the hot oil using a slotted spoon or spider. Fry until golden brown and crisp, about 2–3 minutes per side. Use the slotted spoon to turn rings if necessary. Remove rings to a wire rack set over a baking sheet or to paper towels to drain briefly. Immediately season with a pinch of kosher salt. Repeat with remaining rings, maintaining oil temperature between 350–365°F (175–185°C).

Keep warm

If making ahead, keep cooked rings in a single layer on a wire rack in a 200°F (95°C) oven for up to 15–20 minutes to keep crisp while finishing remaining batches.

Roasted Garlic Aioli

Roast garlic

Preheat oven to 400°F (200°C). Slice about 1/4 inch off the top of the garlic bulb to expose cloves. Place bulb on a piece of foil, drizzle with the teaspoon of olive oil, wrap foil snugly and roast for 30–40 minutes until cloves are soft and caramelized. Let cool slightly, then squeeze roasted garlic cloves from their skins into a small bowl (should yield about 1 to 1 1/2 tablespoons).

Mix aioli

In a small bowl, combine the mayonnaise, roasted garlic (smashed to a paste), lemon juice, Dijon mustard, salt, and black pepper. Whisk until smooth and taste: adjust seasoning with more lemon or salt if desired. For a thinner consistency, whisk in 1/2 teaspoon additional olive oil or a few drops of water. Refrigerate at least 15 minutes to let flavors meld.

Serve

Spoon the aioli into a small serving bowl. Serve chilled or at room temperature alongside the hot onion rings for dipping.