Set up your grill for even medium-high heat. If using a charcoal grill, distribute the coals evenly. If using a gas grill, heat both sides evenly.
In a mixing bowl, whisk together the olive oil, brown sugar, paprika, salt, cumin, coriander, cayenne and lime zest and juice. Add the shrimp and allow to marinate for 15 minutes at room temperature and up to 3 hours refrigerated.
Remove the shrimp from the marinade and place on a cooling rack in a single layer. Put the cooling rack on the grill and cook the shrimp, pulling the cooling rack off the grill to flip them, until charred and cooked through, 2 to 3 minutes per side.
To serve: Add the shrimp to a platter and garnish with lime wedges.