Pat cod filets dry with paper towels and lightly season both sides with salt and pepper. Use a scant teaspoon of flour to very lightly dust one side of cod filets.

Melt 2 tablespoons butter in a large skillet over medium high heat. When butter stops bubbling, add cod filets, floured side down. Cook undisturbed, until a light brown color develops, about 3 minutes. Carefully remove filets and keep warm.

Cook lemon slices in the same skillet for 2 to 3 minutes, turning to cook evenly, and add shallots and capers. Cook about 1 minute more.

Stir in white wine; cook about 1 minute, scraping up any browned bits. Add chicken broth, chopped parsley, and lemon juice; cook about 4 minutes.

Return cod filets to the skillet, floured side up. Cook in the sauce until internal temperature reaches 145°F (63°C). Remove and keep warm.

Remove about 1/4 cup of liquid from skillet; allow to cool slightly.

Add remaining 2 tablespoons butter to skillet and stir until melted.