Prep the Fish:
Pat Dover sole fillets dry with paper towels. Season both sides with salt and pepper. Lightly dredge in flour, shaking off any excess.
Sear the Sole:
In a large skillet over medium-high heat, heat olive oil and 1 tbsp butter until hot but not smoking. Add fillets and cook for 2–3 minutes per side, or until golden and cooked through. Carefully remove fish from pan and set aside on a warm plate.
Make the Sauce:
In the same pan, lower heat to medium. Add garlic and sauté for about 30 seconds. Deglaze with white wine (if using), scraping up any browned bits. Let reduce for 1–2 minutes. Stir in lemon juice, capers, and remaining tablespoon of butter.
Finish and Serve:
Spoon the lemon caper sauce over the fish. Sprinkle with chopped parsley and serve with lemon wedges.
