1. Shell and devein shrimp; save shells. Rinse shrimp. Cut into 1/2-inch pieces.
2. In a 5- to 6-quart pan, combine shrimp shells, 5 cups broth, onion, celery, carrot, bay leaves, and white peppercorns. Bring to a boil over high heat, cover, and simmer for 30 minutes. Pour broth through a strainer into a 2-quart glass measure or bowl. If needed, add more broth to make 5 cups.
3. Melt butter in same pan over medium heat. Add garlic and stir just until limp, 1 to 2 minutes. Stir in flour.
4. Off the heat, whisk broth and half-and-half into flour mixture. Stir over medium-high heat until boiling, then boil for about 2 minutes. Add shrimp and stir until pink, about 1 minute.
5. Add salt and pepper to taste. Ladle into bowls; garnish with dill and shrimp.