In a small bowl, stir together the mayonnaise, lemon juice, Dijon mustard, garlic, smoked paprika, salt, and pepper until smooth. The sauce should look creamy and thick enough to spread easily onto the buns without dripping. Set aside so the flavors settle together while you prepare the burgers.

Pat the halloumi slices dry with paper towels. This helps the cheese form crisp golden edges instead of steaming in the pan. If the slices still feel wet from the brine, dry them a little longer before frying.

Heat a skillet over medium heat and add a thin layer of olive oil. Place the halloumi into the pan and cook for 2-3 minutes per side until deeply golden. The cheese should hiss lightly at the edges and release cleanly from the skillet once ready to flip.

Slice the buns and toast them lightly until the inside turns pale golden while still staying soft in the center. Avoid over-toasting since the burgers are easier to eat with softer bread.

Spread the smoked aioli onto the bottom half of each bun. Layer with lettuce, tomatoes, fried halloumi, red onion, and dill pickles. Add more aioli to the top bun before closing the burgers gently.

Serve the halloumi burgers hot with French fries on the side. They are best eaten while the cheese still has crisp edges and the buns are lightly toasted.