Add the potatoes, carrots and stock to a saucepan over high heat. Bring to a boil and cook for 8 to 10 minutes, just until the vegetables are tender. Strain the stock into a bowl and place the vegetables in a separate bowl.
Heat a large stock pot over medium heat and add the butter and olive oil. Add the lobster tails and claws and cook for only 2 to 3 minutes, just until slightly opaque and red. (If desired, you can add the shells in too to get more flavor, just make sure to remove all the pieces.) Remove the lobster and place it on a plate. Chop the meat from the tails. Leave the claws intact (if you wish!) to serve on top of the soup. You might have to cut a few in half to have enough enough for topping.
Add the onions and thyme to the butter and olive oil and stir well to coat. Throw in a pinch of salt and pepper. Cook the onions until they are soft and translucent, about 5 minutes. Stir the flour into the onions to create a roux. Cook the roux for 3 to 4 minute until it’s golden and fragrant. Add the tomato paste and stir well, cooking for another minute or so.
Pour in the sherry and cook until it’s reduced by half. Add in the reserved stock slowly, stirring while doing so. Add in the potatoes and carrots. Bring the mixture to simmer so it thickens slightly. Add the chopped lobster tails back into the mixture.
Turn off the heat. Very carefully pour the mixture into a blender. Cover the blender and hold a towel over top. Blend the soup on low speed until it is pureed. If you wish, you can also use an immersion blender to do this step! Pour the mixture back into the pot.
Stir in the cream. Taste and add the salt and pepper, adding more if needed. Serve the soup in bowls and top with the lobster claw meat and fresh dill.
To make the lobster cappuccino, use a milk frother to froth about 1/4 cup portions of the cream. Spoon the lobster bisque into a bowl, mug or cup. You can add the claw meat at this point. Spoon the frothed cream on top. Sprinkle fresh dill and smoked paprika on top. Serve immediately!