Dredge sole in flour and place in bowl with egg mixture.
Heat clarified butter in sauté pan until just below smoking point. Add sole fillets, reduce heat to medium. After 2 minutes, turn and continue cooking another 2 minutes.
Place fillets on a warm plate and squeeze a little lemon juice on top.
Add shallots and capers to sauté pan until softened. Add white wine and reduce by half. Add the remaining lemon juice and butter and whisk together. Season with salt and pepper to taste.