Pat the shrimp dry with paper towels, then season lightly with salt and pepper. Set aside.
In a small bowl, whisk the eggs until smooth. On a plate, spread out the flour for dredging.
Dredge each shrimp in the flour, tapping off excess, then dip into the beaten eggs, letting the excess drip off.
Heat a generous splash of olive oil and 1 tablespoon of butter in a large skillet over medium heat until shimmering and fragrant.
Add the coated shrimp in batches, making sure not to overcrowd the pan. Fry each side for about 2 minutes until golden and crispy, hearing a gentle sizzle and seeing the batter turn a deep golden hue.
Use tongs to carefully flip the shrimp, watching the batter crisp up evenly on both sides and the shrimp turn opaque and pink.
Transfer fried shrimp to a paper towel-lined plate to drain excess oil, then repeat with remaining shrimp.
Once all shrimp are cooked, reduce the heat slightly. Pour the white wine into the skillet, scraping up any browned bits from the bottom, and simmer for about 1 minute until slightly reduced.
Add the fresh lemon juice and remaining 2 tablespoons of butter, swirling the pan until the butter melts and creates a shiny, bright sauce.
Return the fried shrimp to the skillet, tossing gently to coat them in the lemon-butter sauce for about 30 seconds, until heated through and well coated.
Serve the shrimp immediately, garnished with chopped parsley and lemon wedges on the side for extra brightness.
