Preheat a grill to high heat.
Toss the shrimp shells with 1 tablespoon of the olive oil and spread them on a piece of heavy-duty foil or a grill-safe pan.
Grill the shells for 5 to 6 minutes, tossing occasionally, until deeply charred and fragrant.
Toss the peeled shrimp with the remaining olive oil, salt, and pepper. Grill for 90 seconds per side, until opaque, and set aside for serving.
Transfer the grilled shells to a large stockpot along with the onion, celery, carrot, and garlic.
Stir in the tomato paste and cook over medium heat for 1 to 2 minutes, until fragrant.
Add the water, bay leaves, and peppercorns. Bring to a boil, then reduce to a gentle simmer.
Simmer uncovered for 25 minutes, until the broth has taken on a deep amber color.
Strain the broth through a fine-mesh sieve, discarding the solids. Season with salt to taste.
Ladle the hot broth into bowls, add the grilled shrimp, and garnish with fresh parsley.