Combine all pesto ingredients in a blender or food processor; blend. Drizzle in more olive oil or water, if needed, until you get a salsa-like consistency. Season to taste with salt and pepper; set aside. Heat grill to medium-high heat (400°F). Brush halibut and grill surface with oil; grill 5 to 7 inches from heat about 8 minutes, turning once during cooking. Cook just until fish is opaque throughout. Season with salt and pepper. To assemble tacos: Char tortillas on grill or grill pan. Top each taco with a big pinch of shaved red cabbage. Break halibut into chunks and distribute evenly between tortillas. Top with a generous spoonful of pesto, a sprinkle of extra cotija cheese, and a lime wedge.
Alaska Halibut can also be sauteed, roasted or broiled, cooking just until opaque throughout.