Pat the shrimp dry with paper towels and set up your dredging station with flour in a shallow dish and beaten eggs in a separate bowl.
Dredge each shrimp in the flour, then dip into the beaten eggs, ensuring an even coating. Place the coated shrimp on a plate as you go.
Heat a large skillet over medium-high heat and add 2 tablespoons of butter and 2 tablespoons of olive oil until shimmering and fragrant, about 30 seconds.
Carefully lay the coated shrimp in the hot skillet, working in batches if needed, and cook for about 2 minutes per side until golden brown and crispy.
Remove the cooked shrimp from the pan and set aside on a plate, keeping them warm.
Add the minced garlic to the same skillet and cook until fragrant, about 30 seconds, stirring constantly to prevent browning.
Deglaze the pan with white wine, scraping up any browned bits from the bottom, and cook until slightly reduced, about 1 minute.
Stir in the lemon juice and a pinch of salt, then let the sauce simmer for 2-3 minutes until bright and slightly thickened.
Return the shrimp to the skillet, spooning the lemon sauce over them, and cook just until heated through, about 1 minute.
Sprinkle the chopped parsley over the dish and give everything a gentle toss to combine. Serve immediately with lemon wedges on the side.
