Prepare the Lobster Shells: Split or crack the lobster shells to expose all the flavor. Leave any residual meat — it enhances richness.
Sauté Aromatics: Heat olive oil or butter in the stockpot over medium heat. Add onion, celery, carrot, and garlic. Cook for 5–7 minutes until softened.
Add Tomato Paste & Wine: Stir in tomato paste, cooking 1–2 minutes. Pour in white wine, simmer 3–4 minutes to reduce slightly.
Add Lobster Shells: Add lobster shells and stir well.
Add Water & Herbs: Pour in cold water to cover shells (about 8–10 cups). Add bay leaf, thyme, parsley, and peppercorns.
Simmer Gently: Bring to a boil, then reduce heat to low. Simmer uncovered for 30–45 minutes.
Strain the Stock: Strain through a fine-mesh strainer into a bowl or container. Press gently on solids to extract maximum flavor.
Cool & Store: Allow to cool before refrigerating (up to 3–4 days) or freezing (up to 3 months).