Rinse the shrimp shells and heads in a large colander under cold running water.
Put all the ingredients in a heavy medium stockpot. Add enough water to cover by 1 inch. Bring to a boil over high heat, skimming from time to time to remove the foam that forms on the surface. Reduce the heat to medium-low. Simmer for 45 minutes.
Strain through a fine-mesh strainer into a large bowl. Cool completely. Cover and refrigerate. (The stock can be refrigerated for up to three days. Or freeze in airtight containers for up to two months.)
Yield: 3 quarts