Heat a saute pan over medium-high heat. Add 1 tablespoon oil and heat to the verge of smoking. Next, mix the salt and pepper evenly into the flour and coat both sides of each fillet of fish. Then add to the pan, cooking until browned, 2 to 3 minutes. Flip and repeat on the second side until golden brown, 2 to 3 minutes. Repeat with each fillet, holding the cooked fillets warm, covered with foil on a plate, until serving. Additional oil may be needed during the process.

After searing the fish, add the wine to the pan to deglaze. Allow the wine to reduce by half, 3 to 4 minutes, then add the stock and reduce by three-quarters volume, resulting in 1 cup sauce. This reduction will take 4 to 5 minutes. Then add the mushrooms, herbs and garlic. Stir and allow to finish, reducing by half again, a final 2 to 3 minutes. Remove from the heat and whisk in the butter until creamy. Finish the fillets with the pan sauce and serve.