Separate garlic cloves into a bowl; place another bowl on top. Shake until all peels separate from cloves, about 30 seconds, being careful not to shake too hard. Mince garlic cloves.

Melt butter in a sauté pan over medium heat; add minced garlic. Cook, stirring occasionally, until golden brown, 2 to 3 minutes; transfer to a small bowl and set aside.

Pat thawed shrimp dry with paper towels; add to a large mixing bowl.

Combine rice flour, paprika, salt, and cayenne pepper in a small bowl; sprinkle over shrimp and toss until completely coated using a large spoon or spatula.

Heat olive oil in a nonstick skillet over medium-high heat. Add shrimp in a single layer, in batches, and cook until browned and just barely cooked through, 2 to 3 minutes per side. Add some garlic butter; cook for 30 seconds more. Repeat with remaining shrimp and garlic butter. Serve immediately.