Ingredients

Shells from 4 cooked lobsters, including carapaces 

2 tablespoons olive oil 

2 small onions, quartered 

2 small carrots, peeled and cut into 1-inch pieces 

2 celery stalks, cut into 1-inch pieces 

4 garlic cloves 

1 small fennel bulb, trimmed and quartered (optional) 

1 can (14 1/2 ounces) whole peeled plum tomatoes, chopped, including juice 

2 cups dry white wine (optional) 

8 whole black peppercorns 

6 fresh thyme sprigs 

6 fresh flat-leaf parsley sprigs 

1 bay leaf 

Preparation

Remove head sacs (behind eyes) in carapaces; discard. Remove any green tomalley or red roe; reserve for another use or discard. Wrap shells in a clean kitchen towel. Using a rolling pin, meat pounder, or hammer, break shells (some large pieces might remain).

Heat oil in a Dutch oven or stockpot over medium heat until hot but not smoking. Add shells; cook until fragrant (do not let blacken), about 3 minutes.

Stir in onions, carrots, celery, and garlic, and fennel (if desired). Cook, without stirring, until vegetables begin to brown, about 3 minutes. Add tomatoes, wine (if desired), peppercorns, thyme, parsley, and bay leaf.

Fill pot two-thirds with cold water (about 4 1/2 quarts). Bring to a boil. Reduce heat; simmer. Skim froth from surface with a ladle. Cook until broth is aromatic and flavorful, about 1 hour 45 minutes.

Carefully pour stock through a fine sieve set over a large bowl or container. Discard solids; let stock cool completely. If not using immediately, refrigerate in airtight containers up to 3 days, or freeze up to 2 months.