Rinse the dover sole fillets and pat dry with paper towels. Season both sides of the fish with salt and pepper to taste
Place the flour on a plate and lightly coat each fillet shaking off excess.
In a large skillet, heat 2 Tbsp. of butter and the olive oil over medium high heat.
Once the butter is melted and foamy, add the fillets. Cook for 3-4 minutes on one side until golden brown, then carefully flip and cook for another 2-3 minutes.
Remove the fish from the pan and set aside on a warm plate.
MAKE THE SAUCE: Add the wine to the same pan, scraping up any browned bites from the bottom of the pan. Let it simmer for 2-3 minutes until slightly reduced. Stir in the chicken stock and continue cooking for another 3-4 minutes.
Add the remaining butter and lemon juice to the skillet whisking until the sauce is glossy.
Return the fish to the skillet just to heat through, spooning the sauce over the fillets.
Sprinkle with the Italian parsley. Serve with lemon slices.