Melt the butter in a large stockpot over medium heat
Add the onions, celery, and carrots. Cook for 8-10 minutes until softened but not browned.
Stir in the garlic and tomato paste (if using) and cook for 1-2 minutes.
Add the lobster shells and stir everything together for 3-5 minutes to bring out the flavour.
Pour in the white wine (if using) and let it reduce for about 2 minutes.
Add the bay leaves, peppercorns, parley, thyme, and cold water.
Bring ust to a gentle boil, then imediately reduce to a gentle simmer.
Simmer 45-60 minutes. Avoid simmering much longer, as the stock can become bitter.
Strain through a fine-mesh sieve, pressing gently on the vegetables and shells to extract the flavourful liquid.