Pat the sole fillets dry with paper towels. There is a lot of moisture in Petrale sole, so you might have to pat them dry twice. Lightly salt the fillets on both sides.
Heat oil in a large, stick-free skillet on medium-high heat. Once the oil is hot, carefully add the fillets to the pan. Brown the fillets gently on both sides. The fish is cooked when it flakes easily and is no longer translucent. Sole fillets will cook up very quickly, no more than a few minutes on each side, so don’t walk away from the pan while cooking. Once done, remove the fillets from pan and place on a warm plate.
Add shallots to the pan and sauté until soft.
Add white wine to the pan with the shallots to deglaze the pan, and scrape up the browned bits at the bottom of the pan.
Add butter and gently swirl to make a sauce. Add herbs, and squeeze a little lemon juice into the sauce. Spoon over the sole.