Pat flounder fillets completely dry with paper towels - this is crucial for browning. Mix flour with 1/2 teaspoon salt and the pepper in a shallow dish. Lightly dredge each fillet, shaking off excess flour.

Heat olive oil and 2 tablespoons butter in a large skillet over medium-high heat until the butter stops foaming. Add fillets in a single layer (work in batches if needed) and cook 2-3 minutes per side until golden and just opaque in the center. Transfer to a warm plate and tent with foil.

Reduce heat to medium. Add remaining 2 tablespoons butter to the skillet. Once melted, add garlic and cook 30 seconds until fragrant but not browned. Pour in wine and simmer 2 minutes, scraping up any browned bits, until slightly reduced.

Stir in lemon zest, lemon juice, and remaining 1/4 teaspoon salt. Simmer 1 minute more. Taste and adjust - the sauce should be bright and buttery, not too tart.

Return fish and any accumulated juices to the pan, spooning sauce over top for 30 seconds to warm through. Transfer to plates, drizzle with remaining sauce, and sprinkle with parsley. Serve immediately with crusty bread or rice to soak up every drop.