Start by making the stock. For this, you will need to wash the shells to remove any dirt and debris. If you have larger pieces, then break them into smaller ones. The easiest way is to put the pieces in a ziplock bag and use a rolling pin to break them.
Preheat your oven to 400 degrees Fahrenheit. Take a large skillet. Add the shells and heat them inside the oven to extract more flavors of the crab.
You will need to cover the shells and simmer them for an hour. Transfer the shells in a large stockpot with an inch of water. Heat the shells on medium to high. If you spot bubbles of air rising to the surface, lower the heat to medium. Remember not to boil the water. Let it foam.
Now, add the carrots, onion, thyme, bay leaves, parsley, celery, tomato paste, wine, and peppercorns to the stock.
Simmer the stock on medium heat and then lower the heat to simmer for another 30 minutes. Some foam might develop at this stage. Skim off the extra foam.
Add salt and turn off the heat.
Separate the larger solids from the stock using a fine-meshed or spider meshed strainer. You have a bowl full of stock right before you for later use. Self-prepared stock adds some extra flavor to the bisque.
Now, in a 6-quart saucepan, melt the butter over a medium flame. Add the shallots. Cook them until they are light brown. This step will take about 5 to 6 minutes.
To this, pour wine, rice, stock, and tomato paste. Simmer the mixture for 25 minutes on medium heat and reduce the heat to continue. Remove the pan and set it aside to cool.
Add two-thirds of the meat to the soup and blend all of them in batches. Puree the soup evenly. Transfer it back to the pan.
At this stage, pour the cream and heat the soup gently. Add the rest of the meat pieces. Sprinkle salt and pepper to taste. Your dish is ready.