Pat the cleaned calamari tubes and tentacles very dry with paper towels. If tubes are whole, slice into 1/2-inch rings. Place in a bowl and refrigerate while you prepare the batter to keep them cold.

Make dredge and wet mix

In a shallow bowl or pie plate, whisk together the all-purpose flour, cornstarch, 1 teaspoon fine sea salt, 1/2 teaspoon black pepper, and 1/2 teaspoon sweet smoked paprika. In a second shallow bowl, whisk the egg with 1/4 cup milk until homogeneous.

Heat the oil

Pour about 3–4 cups vegetable oil into a heavy, deep skillet or medium Dutch oven to a depth of about 2 inches. Heat over medium-high heat until the oil reaches 350°F (175°C). If you don't have a thermometer, test by dropping a small pinch of flour into the oil — it should sizzle and float immediately.

Dredge and fry in batches

Working in small batches to avoid crowding (about 6–8 rings per batch), dip the calamari pieces into the egg-milk mixture, letting excess drip off, then dredge thoroughly in the flour-cornstarch mixture, pressing to adhere. Shake off excess flour and gently lower into the hot oil using a slotted spoon or spider. Fry 1 to 1 1/2 minutes, turning once, until golden and crisp. Do not overcook — calamari cooks quickly and becomes rubbery if left too long.

Drain and season

Remove fried calamari with a slotted spoon and transfer to a wire rack set over a baking sheet or paper towels. Immediately sprinkle lightly with a pinch of salt while still hot. Keep warm in a 200°F (95°C) oven if needed while frying remaining batches.

Finish

When all batches are fried, give a final quick toss on the rack to redistribute any excess oil. Transfer to a serving platter.

Serve

Serve the hot fried calamari alongside lemon wedges and the remoulade sauce. Place the mixed greens on the plate as described below.

Mixed Greens

In a small bowl, whisk together 1 tablespoon extra-virgin olive oil, 1 teaspoon fresh lemon juice and 1/4 teaspoon fine sea salt. Toss the mixed salad greens gently in the dressing just before plating so they remain crisp. Arrange a small mound of dressed greens on each appetizer plate next to the calamari.

Spicy Creamy Remoulade

In a small bowl, combine 1/2 cup mayonnaise, 1 teaspoon Creole or Dijon mustard, 1 teaspoon prepared horseradish, 1/2 teaspoon hot sauce, 1 teaspoon lemon juice, 1 teaspoon chopped capers, 1 teaspoon very finely chopped cornichon or dill pickle, 1 teaspoon finely chopped fresh parsley, 1/4 teaspoon smoked paprika, 1/2 teaspoon minced garlic, 1/4 teaspoon salt and 1/8 teaspoon black pepper. Whisk until smooth and taste; adjust seasoning or heat to preference. Chill for at least 15 minutes to let flavors meld.