For snapper fillets with perfectly crisp skin, chef Jennifer Carroll only seasons the flesh side before laying the fish on a very hot grill. Slideshow: More Grilled Fish Recipes
In a medium bowl, combine the herbs with 1/3 cup of the olive oil, the lemon zest and lemon juice; season the gremolata with salt and pepper and mix well.
Light a grill or preheat a large cast-iron grill pan. In a large bowl, toss the bell peppers and scallions with 2 tablespoons of the olive oil and season with salt and pepper. Grill over moderately high heat, turning, until golden and tender, 5 to 8 minutes. Halve the scallions crosswise and cut the peppers lengthwise into 1/2-inch strips.
Brush the grill with oil. Rub only the flesh side of the fish with the remaining 2 tablespoons of oil and season with salt and pepper. Grill the snapper skin side down over moderately high heat until golden, 3 to 4 minutes. Flip and cook until opaque throughout, about 2 minutes longer. Transfer to plates.
In a large bowl, toss the lettuces and the grilled peppers and scallions with the chile and 1/4 cup of the gremolata. Spoon the salad over the fish and serve the remaining gremolata on the side.
The gremolata can be refrigerated for 3 hours.
Tangy Sauvignon Blanc.