Makes about 3 quarts
Rinse the shrimp shells and heads in a large colander under cold running water and allow to drain.
In a large stockpot, heat the oil over medium-high heat. When hot, add the shrimp shells and cook, stirring occasionally, until shells are pink and toasty-fragrant, 4 to 6 minutes. Add the water and all 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 stock is flavorful, 45 minutes to 1 hour.
Strain the stock through a fine-mesh sieve into a large heatproof bowl and allow to cool completely, then cover and refrigerate for up to 3 days. (Alternatively, the stock may be placed in airtight containers and frozen for up to several months.)
Cook's note: If desired, you can easily double the ingredient amounts for a larger batch of stock, and then freeze until needed. Also, to save space in the freezer, you can reduce the stock further after straining and discarding solids.