Gather all your ingredients and pat the shrimp dry with paper towels. Beat the eggs in a shallow dish and season the flour with a pinch of salt and pepper in another dish.
Dip each shrimp into the beaten eggs, letting the excess drip off, then coat thoroughly with the seasoned flour. Place the coated shrimp on a plate as you go.
Heat the butter and olive oil in a large skillet over medium heat until the butter melts and the mixture begins to shimmer.
Carefully place the coated shrimp in the skillet in a single layer. Cook for about 2-3 minutes per side until the coating is golden and crispy, and the shrimp are opaque. Flip gently with tongs as needed.
Remove the cooked shrimp from the skillet and set aside. Pour the white wine into the pan, scraping up any browned bits from the bottom with a wooden spoon, and let it simmer for 2 minutes to reduce slightly.
Add the lemon juice and lemon zest to the skillet, stirring to combine. Then, whisk in the remaining butter until the sauce is glossy and slightly thickened.
Return the shrimp to the skillet, tossing gently to coat in the lemon-butter sauce. Cook for another minute until heated through and flavorful.
Transfer the shrimp to a serving plate, spoon the sauce over the top, and garnish with chopped parsley. Serve immediately with lemon wedges and crusty bread if desired.