1. Place shrimp shells and heads in a large colander and rinse under cold running water.

2. Place all ingredients in a heavy 6-quart stockpot. Add 4 quarts water, and bring to a boil over medium-high heat, skimming surface occasionally. Reduce heat to medium-low and simmer, uncovered, for 45 minutes, continuing to skim surface occasionally.

3. 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.