Heat a medium sized skillet on medium-high heat with coconut oil. Once hot, add the sole and pan fry for about 2 minutes on each side or until fully cooked and flakey.

Remove from pan, and add the olive oil, lemon juice, and capers, stir for about 5 minutes. Increase the heat to high, and let simmer until the sauce thickens slightly, and then add the minced parsley right at the end. Pour over the cooked sole and serve.