Prep the shrimp. Pat the shrimp very dry with paper towels.
Moisture prevents crisping, so this step matters. If using large shrimp, you can butterfly them slightly for more surface area.
Mix the coating. In a shallow bowl, combine panko, Parmesan, paprika, garlic powder, onion powder, salt, and pepper. In another bowl, beat the egg.
Coat the shrimp. Dip each shrimp in egg, let excess drip, then press into the panko mixture to coat on both sides.
Set coated shrimp on a plate. Work in batches so crumbs stay crisp.
Crisp the shrimp (stovetop). Heat a large nonstick skillet over medium-high. Add a thin film of oil.
Cook shrimp 2–3 minutes per side until golden and opaque. Don’t crowd the pan. Transfer to a wire rack to keep the bottoms from steaming.
Or air-fry. Air fryer at 400°F (205°C).
Spray basket, arrange shrimp in a single layer, mist tops with oil, and cook 6–8 minutes, flipping halfway, until crisp and cooked through.
Make the dressing. Whisk yogurt, mayo, olive oil, Dijon, anchovy, garlic, lemon juice, Worcestershire, and Parmesan until smooth. Season with salt and pepper. Adjust lemon for brightness and anchovy for savoriness.
Toss the greens. In a large bowl, toss romaine with just enough dressing to lightly coat.
Save extra dressing for drizzling inside the wrap.
Warm the tortillas. Briefly warm each tortilla in a dry skillet or microwave until pliable. Warm wraps roll better and don’t tear.
Assemble. Lay down a bed of dressed romaine, add a line of crispy shrimp, then drizzle a bit more dressing. Add optional extras like avocado or tomatoes.
Finish with a sprinkle of Parmesan.
Wrap it up. Fold the sides in, roll tightly from the bottom, and place seam-side down. For extra crunch and warmth, sear the wrapped tortilla in a dry skillet 1–2 minutes per side.
Serve. Slice in half on a bias. Add a wedge of lemon on the side for a fresh squeeze.