Step 1

Prepare a grill for medium-high heat; lightly oil grate. Mix shallot, 1 Tbsp. lime juice, and ½ tsp. brown sugar in a small bowl to combine; season with salt and pepper. Set aside.

Step 2

Pat fish dry with paper towels and season all over with salt and pepper. Toss green beans with 1 Tbsp. oil on a rimmed baking sheet; season with salt and pepper. Grill beans, turning often (be careful not to let them fall through the grate), until softened and charred in spots, about 2 minutes. (To keep the green beans from falling through the grate, place a wire rack crosswise on the grill to create smaller squares and extra insurance.) Transfer to a platter. Pat fish dry again and rub fillets with 2 Tbsp. oil. Gently place on grate, skin side down, and grill, undisturbed, until flesh is opaque except for the thickest part, 6–8 minutes. Carefully slide a thin metal spatula underneath fillet, trying not to tear skin, and turn over; grill 1 minute longer. Place, skin side up, on platter with green beans.

Step 3

Whisk fish sauce, remaining ¼ cup oil, remaining 3 Tbsp. lime juice, and remaining 1 Tbsp. brown sugar in a small bowl until sugar is dissolved. Drizzle over fish and beans and scatter shallot mixture over. Let marinate at least 15 minutes and up to 2 hours. Cover and chill if holding longer than 30 minutes. Bring to room temperature before serving.

Step 4

Top with peanuts just before serving.