Preheat the oven to 200 degrees. Line a baking sheet with paper towels.
Rinse the fish in cold water and pat them dry; season both sides of the fish with sea salt and freshly cracked pepper, to taste. Pour the flour onto a large plate then season with a bit more sea salt and freshly cracked pepper; mix well. Dredge both sides of the fillets in the flour so they are lightly coated.
Heat half of the olive oil in a large sauté pan over medium high heat. Once the pan is HOT add half of the fish fillets. Cook for 2 minutes then carefully flip with a spatula; cook for another minute or so. Remove from the pan and place on a baking sheet covered with paper towels. Place into the preheated oven. Add the remaining oil to the hot skillet then add the remaining sole and cook for 2 minutes before flipping and cooking for another minute, or until cooked through. Place the fish on the paper towel lined baking sheet and place into the oven.
Add the chicken broth to the hot pan and stir, making sure to scrape up the browned bits. Add the lemon juice and capers then continue to cook until reduced, about 2 minutes. Add the butter and stir until melted and well combined.
Place the sole on a serving plate then spoon the sauce on top. Serve immediately. Enjoy.