Pour olive oil into a large pot. Place over medium heat.
When oil is hot and shimmering, add lobster shells, thyme sprigs and bay leaf. Sauté until shells turn bright red, about 5 minutes.
Stir in onion, celery, carrot and garlic. Cook until softened, about 8 minutes.
Add tomato paste. Cook, stirring, until it darkens slightly, about 2 minutes.
Pour in cognac. Simmer cognac over medium heat for 2 to 3 minutes, stirring often, until the alcohol cooks off and the liquid reduces slightly. (If cooking on a gas stove, be careful adding and cooking the cognac, it can flame up if it touches the open flame.)
Add white wine. Cook to reduce by half, about 3 minutes.
Add fish stock. Bring to a gentle simmer.
Stir in jasmine rice. Cook for 20 minutes to extract flavor and naturally thicken.
Remove shells, thyme and bay leaf. Discard these.
In batches, purée broth in a blender until smooth. Strain through a fine-mesh sieve back into pot.
Return bisque to low heat.
Whisk in heavy cream and unsalted butter until the soup is silky and cohesive.
Fold in chopped lobster meat, warming gently for 2 minutes.
Taste. Season with salt and black pepper, to taste .
Ladle into warmed bowls and garnish with a small sprig of fresh thyme.