Add the potatoes, carrots and a couple tbsp seafood stock to a saucepan over high heat. Bring to a boil and cook for 8 to 10 minutes, just until the vegetables are tender. Stock should evaporate, then place softened vegetables to the side.
Heat a large stock pot over medium heat and add the butter and olive oil. 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 port/sherry and cook until it’s reduced by half. Add in the rest of the seafood 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. Stir in the cream.
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.
Taste, and add more salt and pepper, if needed. Serve the soup in bowls and top with the lobster claw meat and fresh dill.