Step 1

Combine all pesto ingredients in a blender or food processor and 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.

Step 2

Heat grill to medium-high heat (400F). Brush Alaska halibut and grill surface with oil; grill 5-7 inches from heat for about 8 minutes, turning once during cooking. Cook just until fish is opaque throughout. Season with salt and pepper.

Step 3

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.Cook’s tip: Alaska halibut can also be sautéed, roasted or broiled, cooking just until opaque throughout.