1. Rinse the shrimp shells and heads in a large colander under cold running water and allow to drain.
2. In a large stockpot, heat the oil over medium-high heat. When hot, add the shrimp shells and cook, stirring occasionally, until the shells are pink and toasty-fragrant, 4 to 6 minutes. Add the water and all the remaining ingredients and bring to a boil over high heat, skimming any foam that comes to the surface. Reduce the heat to medium-low and continue to cook at a slow simmer until the stock is flavorful, 45 to 60 minutes.
3. Strain the stock through a fine-mesh sieve into a large heat-proof bowl and allow it to cool completely. Cover and refrigerate for up to 3 days before using. (The stock may also be placed in airtight containers and frozen for up to several months.)
Yield: about 12 cups