Using a mortar and pestle, crush 1/2 cup fennel fronds, black and pink peppercorns, garlic, and parsley to a paste. (Or pulse in a food processor.) Stir in 2 tablespoons oil. Rub mixture over fish, inside and out; stuff fish with more fennel fronds, herb sprigs, and greens. Cover with plastic wrap; let stand 30 minutes.
Preheat grill to medium. Season fish generously with salt and pepper. Brush a fish-grilling basket with oil; place fish inside and secure. Grill, covered, turning once, until fish is opaque and flakes when tested with the tip of a knife, 20 to 25 minutes.
Meanwhile, toss fennel bulbs and chiles in a bowl with salt and remaining 2 tablespoons oil. Grill until fennel and chiles are lightly marked and tender (if they start to burn, shift to a cooler area of grill). Arrange fish on a platter; surround with lemon, potatoes, fennel, and chiles (chiles should be eaten with caution). Drizzle with herb sauce; serve immediately.