This is one of my favourite things to eat, i don't use cream in this as i like the clean flavour, but feel free to add a splash if it takes your fancy
Bring a pan of water to the boil, add salt followed by your Lobster, boil for 6 minutes. Remove and place into cold water to cool.
Once cool enough to handle, place lobster on its back and with a chefs knife, cut the lobster from underneath, all the way from the tail to the head. Rinse away any tomally (the soft, green substance found in the body cavity of lobsters) from the head cavities. Remove and refrigerate claw and tail meat.
Heat half of your butter in a large saucepan, add the crushed lobster shells and fry at medium high heat for 5 minutes until colour and smell is maximised.
Add your chopped fennel, carrot, garlic, shallot, plum tomatoes, thyme, and chilli and cook on a high heat until slightly browned
Chuck in your pernod and burn off the alcohol and reduce by half, then add your tomato paste and paprika and cook out for 5 minutes
Add your pre-made fish stock, bring to the boil and simmer for 30 minutes skimming as required
Pass through a fine sieve and reduce by half or just under sauce consistency and set aside
Carve your lobster up and place in a serving bowl, bring your bisque up to the boil and whisk in your remaining butter, season with salt, black pepper and lemon juice and pour over your lobster tails and serve with some crusty bread and aioli