Season the swordfish on both sides with salt, pepper, and paprika. Drizzle each side with oil to prevent sticking on the grill. Let marinate for 10 to 15 minutes.
Preheat a grill or grill pan on medium heat.
Place all ingredients for the sofrito in a blender or food processor. Blend until smooth. Season with salt and pepper to taste. Set aside.
Grill the swordfish on both sides marking each side well, to an internal temperature of 125 degrees using a thermometer.
Spoon the sofrito (about 1 to 2 tablespoons per portion) over the fish. Garnish with scallions. Serve with bread.