Heat oven to 500 degrees F and arrange rack in upper third.
Place chiles on a baking sheet and roast until blackened and soft, about 10 to 15 minutes. Trim chiles and remove seeds.
Combine chiles, garlic, paprika, lime juice, and vinegar in a blender and blend until smooth and combined, about 1 minute. Add olive oil and blend until thoroughly incorporated and marinade thickens slightly.
Combine marinade and shrimp in a medium nonreactive bowl and toss to coat. Let marinate 20 minutes to 24 hours in the refrigerator.
Heat a large cast iron skillet over medium-high heat. When heated, add half the shrimp and cook until white with a few brown spots, about 1 to 2 minutes per side. Transfer to a serving plate and season with salt. Repeat to cook off all shrimp.
Toss shrimp with cilantro and serve with lime wedges over rice.