Pat the shrimp dry and season lightly with salt and pepper. Spread flour on a plate and lightly dredge the shrimp, shaking off excess for a thin, even coating.
Heat a large skillet over medium-high heat, then add 1 tablespoon of butter and 1 tablespoon of olive oil. Once melted and bubbling, add the shrimp in a single layer.
Sear the shrimp without moving for about 2 minutes, until they turn golden brown on the bottom. Flip carefully with a slotted spoon and cook another 1-2 minutes until fully opaque and pink. Remove the shrimp and set aside.
In the same skillet, add the minced garlic and cook for about 30 seconds until fragrant and slightly golden, stirring constantly to prevent burning.
Deglaze the pan with the white wine or broth, scraping up any browned bits from the bottom. Let it simmer for 2 minutes until the liquid reduces slightly and the aroma intensifies.
Add the rinsed capers, lemon juice, and remaining 2 tablespoons of butter. Stir gently until the butter melts and the sauce becomes glossy and fragrant, about 1 minute.
Return the cooked shrimp to the skillet, tossing gently to coat them in the sauce. Cook for another 30 seconds to reheat and meld flavors.
Remove from heat and let rest for a minute. Serve immediately, spooning the bright, glossy sauce over the shrimp, garnished with lemon slices or parsley if desired.
