Heat oil in a large nonstick skillet over medium-high heat. Sprinkle shrimp with 1/4 teaspoon salt and pepper. Add shrimp to pan; cook 4 minutes, turning once. Remove from pan; keep warm.
Add broth, garlic, and peas to pan; simmer 3 minutes. Combine 1/4 teaspoon salt, pea mixture, mint, and butter in a blender; process until smooth. Add vinegar; pulse to combine. Spoon 1/3 cup pea sauce onto each of 4 plates; top each serving with 5 shrimp.