Add all the ingredients to a food processor or blender, using just 1/4c olive oil to start. Whirl to blend and drizzle more olive oil as necessary until desired consistency is achieved. Serve or store in refrigerator in an airtight container or jar until ready to serve.
Pat halibut steaks dry, rub with olive oil, and season both sides of each steak with salt and pepper.
Grill on one side, about 5 minutes, then flip. Cook until there is nice color on the steaks and the fish is just about cooked through (opaque), being careful not to overcook and dry out. The fish should flake easily with a fork. The time it takes for your halibut to cook will depend on the thickness of your steaks and the temperature of your grill.
Top with Pistachio Pesto and serve over mashed potatoes with lemon wedges.