Heat oven to 350 degrees. In an oven safe pan, melt coconut oil or other fat. Meanwhile season fish with salt and pepper. Place fish in pan (if skin on, place skin side down). Cover with shallots, tomatoes and olives. Bake for 15-20 minutes, or until it easily flakes with a fork.
Remove from oven and top with olive oil and lemon juice. Serve on a plate and add chopped basil.