Shrimp and lobster are the most flavorful shellfish to use here.
Have ready:
Rinse the shells or carcasses and drain well. Wrap larger crab and lobster shells in a kitchen towel and smash them into small pieces with a rolling pin or the spine of a large knife. Heat in a stockpot over medium-high heat:
Add the shells and cook, stirring occasionally, until their color brightens and they become aromatic, 3 to 5 minutes. Add:
Add:
Bring almost to a boil, reduce the heat, and simmer gently, partially covered, for 30 minutes. Strain well. Let cool uncovered, then refrigerate covered. Use within 4 days or freeze for up to 6 months.