Pat the cleaned calamari tubes and tentacles very dry with paper towels. If tubes are large, slice into 1/2-inch rings. Transfer to a bowl and refrigerate uncovered while you prepare the batter for 10–15 minutes to further dry (this helps crispiness).

Make the wet mixture

In a medium bowl whisk together buttermilk (or whole milk) and the large egg until combined. Season lightly with 1/4 tsp of the salt and 1/4 tsp pepper. Add calamari to the mixture and toss to coat. Let sit 5–10 minutes; do not exceed 30 minutes.

Make the dry dredge

In a shallow wide bowl or rimmed tray combine all-purpose flour, cornstarch, remaining 1 3/4 tsp salt, remaining 3/4 tsp black pepper, sweet smoked paprika and garlic powder. Whisk to evenly distribute spices.

Heat the oil

Pour vegetable oil into a heavy-bottomed skillet or Dutch oven to reach about 1 to 1 1/2 inches depth (about 1 cup for a small pan). Heat over medium-high until oil reaches 350°F (175°C). If you don't have a thermometer, test with a small pinch of flour — it should sizzle immediately and brown in about 40–50 seconds.

Dredge and fry

Working in small batches (to avoid overcrowding), remove calamari from the buttermilk mixture allowing excess to drip off. Toss pieces in the flour mixture to coat thoroughly, pressing lightly so the coating adheres. Shake off excess flour and carefully lower into hot oil using a slotted spoon or spider. Fry 1 to 1 1/2 minutes on the first batch until golden and crisp, turning if necessary; tentacles may take slightly longer. Do not overcook — calamari should be tender. Remove with a slotted spoon to a wire rack set over a tray or paper towels to drain. Immediately sprinkle with a pinch of salt. Repeat with remaining calamari, keeping cooked batches warm in a low oven (200°F / 95°C) if needed.

Finish and garnish

Transfer fried calamari to a serving platter. Squeeze lemon wedges over top, sprinkle with chopped parsley if using, and serve hot alongside the smoked pepper aioli.

Smoked Pepper Aioli

In a small bowl combine mayonnaise and Greek yogurt (if using). Whisk in smoked paprika, roasted red pepper purée, minced garlic, minced hot cherry peppers, lemon juice, smoked sea salt and black pepper until smooth and homogeneous.

Taste and adjust: add more minced hot cherry pepper for heat, more lemon for brightness, or a pinch more smoked salt for depth. If the aioli is too thick, thin with 1/2 tsp water or a few drops of olive oil and whisk. Stir in the optional teaspoon of extra-virgin olive oil for shine and a silkier mouthfeel.

Cover and chill for at least 15 minutes to allow flavors to meld. Bring to room temperature just before serving if chilled fully; serve alongside hot calamari.