Pat shrimp dry, then transfer to a medium bowl. Toss shrimp with 1 tsp. paprika, 1 ½ tsp. salt, and a few grinds of pepper.
In a large skillet over medium heat, heat 2 Tbsp. oil. Add shrimp in an even layer and cook, turning halfway through, until cooked through and opaque, 2 to 3 minutes. Transfer to a clean plate.
In same skillet over medium-high heat, heat remaining 1 Tbsp. oil. Cook onion, stirring occasionally, until softened, about 7 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute more.
Sprinkle remaining 4 tsp. paprika all over skillet and cook, stirring, until fragrant, about 1 minute. Slowly pour in broth while stirring, then add tomatoes. Season with 1 ½ tsp. salt and a few grinds of pepper. Bring to a simmer and cook, stirring occasionally until slightly thickened, about 5 minutes.
Stir in sour cream until combined. Return shrimp to skillet and bring to a simmer. Cook, stirring, until just heated through, about 1 minute; season with salt and pepper, if needed.
Top with parsley. Serve over rice.