Heat the olive oil and minced anchovies in a large skillet over medium-high heat, stirring as the oil heats to dissolve the anchovies. Once the anchovies are sizzling, add the sea scallops, and cook without moving the scallops for 2 minutes.
Meanwhile, toss red bell pepper, orange bell pepper, red onion, garlic, lime zest, and lemon zest in a bowl; season with salt and pepper. Sprinkle pepper mixture onto the scallops and continue cooking until scallops have browned, about 2 minutes more. Turn scallops, stir the pepper mixture, and continue cooking until the scallops have browned on the other side, 4 to 5 minutes. Garnish with parsley sprigs to serve.