Separate garlic cloves into a bowl and place another bowl on top. Shake until all of the peels are knocked off the cloves, about 30 seconds, being careful not to shake too hard. Chop peeled cloves into relatively small pieces.
Melt butter in a saute pan over medium heat and add chopped garlic. Cook, stirring occasionally, until golden brown, 2 to 3 minutes. Transfer the garlic and butter into a small bowl and reserve.
Pat thawed shrimp dry with paper towels and add to a large mixing bowl.
Combine rice flour, paprika, cayenne, and salt in a small bowl. Sprinkle over the shrimp and use a large spoon or spatula to toss until completely coated.
Heat olive oil in a nonstick skillet over medium-high heat. Add some shrimp in a single layer and cook until browned and just barely cooked through, 2 to 3 minutes per side. Add some garlic butter and cook for another 30 seconds. Repeat with remaining shrimp and garlic butter. Serve immediately.
Recipe can be made with shell-off shrimp for easier eating but cooking with the shells on is the classic method. I think the best shrimp to use for this is the 21 to 25 per pound size.
All-purpose flour can be used instead of rice.
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