How to Make It
To make the sauce: Heat the oil and anchovies in a large saucepan over medium heat, stirring often, until the anchovies are sizzling and broken down into a paste, about 2 minutes. Add the garlic and cook until it begins to brown around the edges, about 1 minute. Stir in the olives, capers, and red pepper flakes and cook until heated through, about 2 minutes. Stir in the cherry tomatoes and season to taste with the salt and pepper. Cook, stirring occasionally, until the tomatoes begin to break down, about 10 minutes. Set the sauce aside.
Oil a large ridged grilling pan and heat it over medium-high heat. Brush the sea bass on both sides with oil and season with the salt and pepper. Place on the grill, skin side down, and grill until the underside is seared with grill marks, about 3 minutes. Flip the fresh fish over and cook until the other side is seared and the flesh is opaque when pierced in the center with the tip of a small sharp knife, about 3 minutes more. Transfer each fillet to a dinner plate and top with a spoonful of the sauce. Sprinkle with parsley and serve.