In a large pot, combine lobster shells, water, and white wine. Bring to a boil, then reduce heat and simmer uncovered for 20 minutes. The liquid should reduce slightly and take on a pale orange hue. Strain through a fine-mesh sieve, pressing on the shells to extract every drop. Discard solids. You should have about 3 cups of stock.

In the same pot, melt butter over medium heat. Add onion, carrot, and celery with a pinch of salt. Cook, stirring occasionally, until softened but not browned, about 8 minutes. The vegetables should look translucent and smell sweet.

Stir in tomato paste and cook for 2 minutes until it darkens slightly. Sprinkle flour over the vegetables and cook, stirring constantly, for 1 minute to remove the raw flour taste. The mixture will look pasty and coat the vegetables evenly.

If using cognac, add it now and stir until nearly evaporated, about 30 seconds. Gradually whisk in the reserved lobster stock, scraping up any browned bits from the bottom of the pot. Bring to a gentle simmer and cook for 10 minutes until the vegetables are completely tender.

Remove from heat and blend until completely smooth using an immersion blender or in batches in a regular blender. Return to low heat and stir in heavy cream and paprika. Simmer gently for 5 minutes - do not boil or the cream may separate. Taste and adjust seasoning with salt and pepper.

Add the reserved chopped lobster meat and warm through for 2-3 minutes until just heated. Overcooking will make the lobster tough. Ladle into warm bowls and serve immediately.