Saute aromatics: In a large stock pot, saute the onions, carrots, celery, and garlic with vegetable oil until fragrant, about 3 minutes.
Add lobster shells and boil: Next, add the lobster shells, bay leaf, tomato paste (if using), and enough water to cover the shells by 2 inches. I used 8 cups in total. Bring to a boil, then reduce to a simmer for at least 1 hour.
Strain: Once the stock is flavorful, strain the shells and aromatics using a fine mesh strainer optionally lined with cheesecloth.
Storage: Store in the fridge for up to 3 days or freeze for 2 months. Note: Salt is intentionally left out and should be added at the time of use.
