Combine mayonnaise, ketchup, brown mustard, whole grain mustard, minced garlic, paprika, lemon juice, Worcestershire sauce, green onion, diced celery, and fresh parsley in a food processor. Pulse until well blended but still slightly textured—you want it creamy, not completely smooth. Taste and adjust seasoning with salt as needed. Set aside at room temperature while you prepare the shrimp and grill.

In a small bowl, combine garlic powder, smoked paprika, chili powder, onion powder, dried oregano, dried thyme, cayenne pepper, kosher salt, and cracked black pepper. Pat the shrimp dry with paper towels—this is crucial for getting a good sear on the grill. Toss the shrimp with the spice mixture and olive oil until evenly coated, making sure every piece is well seasoned. I like to let the shrimp sit for just a few minutes so the spices can begin to adhere, but don't let them sit too long or they'll release moisture.

Preheat your grill to medium-high heat. While it heats, brush the French bread rolls with melted butter on the cut side. Place the seasoned shrimp directly on the grill grates and cook for about 2 minutes per side—they should be opaque and lightly charred. At the same time, place the buttered rolls cut-side down on the grill for about 1-2 minutes until golden and crispy. Remove everything from the grill immediately once done—shrimp cooks quickly and overcooking makes it tough.

Spread a generous layer of remoulade sauce from Step 1 on the cut side of each toasted roll. Divide the grilled shrimp evenly among the four rolls, piling them on top of the sauce. Layer the shredded lettuce and tomato slices on top of the shrimp, dividing them equally among the sandwiches. Serve immediately while the shrimp is still warm and the bread is crispy.