Set up your dredging station by whisking the eggs in a shallow dish and mixing the seasoned flour in another dish.
Pat the shrimp dry with paper towels, then lightly season with salt and pepper. Dip each shrimp into the eggs, letting excess drip off, then coat thoroughly in the flour mixture.
Heat about 3 tablespoons of oil in a large skillet over medium-high heat until shimmering and hot but not smoking.
Add the coated shrimp in batches, making sure not to overcrowd the pan. Fry for 2-3 minutes per side until golden brown and crispy, then transfer to a paper towel-lined plate to drain excess oil.
In the same skillet, melt 2 tablespoons of butter over medium heat, then add the minced garlic and cook until fragrant, about 30 seconds.
Pour in the white wine and lemon juice, bringing the mixture to a gentle simmer. Let it cook for about 2 minutes until slightly reduced and fragrant.
Return the fried shrimp to the pan, spooning the lemon butter sauce over them. Cook for another minute just to warm the shrimp through and coat them evenly.
Remove from heat and sprinkle with freshly chopped parsley. Squeeze additional lemon juice over for extra brightness if desired.
Transfer the Shrimp Francese to a serving platter, spooning extra sauce over the top. Serve immediately with lemon wedges for an extra zesty touch.
