Make the salsa verde: Combine all of the ingredients, except the oil, in a blender. Blend until smooth, then drizzle the oil in slowly. Season with salt and pepper.
Cook the vegetables: Fire up your grill. Remove the bottom of the cabbage and separate the leaves. Drizzle with oil, salt, and pepper and place on the grill. Cook until nicely charred and wilted, about 2 minutes if grill is hot enough. Remove to a serving dish. Heat the remaining oil in a large skillet. When the oil is shimmering, add the shishitos, tossing frequently. Cook for about 4 minutes. Once they are nicely browned and wilted, add the shallot and garlic and cook for 1 more minute, tossing frequently so as not to get color on these. Add the lemon juice and salt and pepper to taste. Place on top of the cabbage on the serving dish.
Cook the fish: Preheat the oven to 400 degrees. Check the fish completely for scales. Once all have been removed, score the fish diagonally, all the way to the backbone, on both sides. Brush the fish with olive oil and season with salt and pepper. Roast the fish for 20 to 25 minutes, until the flesh around the neck is tender.
Place the fish over the cabbage and peppers on the serving dish, and top liberally with the salsa verde.