Preheat the grill to medium high heat. Rub the swordfish with avocado oil and sprinkle light some salt. Place the swordfish on the grill and cook for approximately 5 minutes per side.
While the fish cooks, heat the coconut oil in a skillet. Add in the onion and cook for 2 minutes until translucent. Next add in the tomato and jalapeno pepper, and mix with onion, cooking for another 2-3 minutes. Remove from heat, stir in the basil and season with salt.
Place the tomato topping on the swordfish and serve immediately.