In a bowl, whisk together paprika, garlic, Italian seasoning, lemon juice, olive oil, pepper, basil, and brown sugar until the mixture is thoroughly blended.
Marinating the Shrimp: 2. Add the shrimp to the marinade, tossing them to ensure an even coating. Make sure the shrimp are well-covered with the marinade.
Cover the bowl and refrigerate the marinating shrimp for a minimum of 2 hours. Be sure to turn them at least once during this time.
Grilling the Shrimp: 4. Preheat your outdoor grill to medium-high heat.
Lightly oil the grill grate, placing it about 4 inches away from the heat source.
Remove the shrimp from the marinade, draining off any excess liquid, and discard the remaining marinade.
Place the shrimp on the preheated grill, turning them once.
Grill the shrimp until they become opaque in the center, which usually takes about 5 to 6 minutes.
Once cooked, serve the grilled shrimp immediately.