1 pound (about 8 cups) shrimp shells and heads
1 coarsely chopped onion
1/2 cup coarsely chopped celery
2 coarsely chopped carrots
3 cloves garlic, smashed
3 bay leaves
1 teaspoon black peppercorns
1 teaspoon dried thyme
2 teaspoons salt
Place all ingredients in a heavy 6-quart stockpot. Add 4 quarts water, and bring to a boil over medium-high heat. Reduce heat to medium-low and simmer, uncovered, for 45 minutes.
Remove stock from heat and strain through a fine-mesh sieve set over a large bowl; let cool completely. Refrigerate stock up to 3 days or freeze in an airtight container, up to 2 months.