Remove meat from the crayfish tails and cut into bite-sized pieces. Reserve the shells for making the crayfish stock or infusing the stock.
For the Crayfish stock, rinse the carcass/shells. Cook the carrot, celery rib, garlic cloves, bay leaf, and thyme sprig in olive oil in a 6-8 litre pot over moderate heat until softened. Stir in the carcass/shells and water. Bring to a boil and simmer until reduced to about 61/2 cups, about 11/2 hours. Strain through a cheesecloth-lined fine sieve. OR For the Infused stock, place the chicken stock and the carcass/shells into a large, heavy based saucepan and bring to the boil. Reduce heat to a simmer and cover with a lid to infuse for 5 minutes, then strain.
For the Risotto, place a medium sized, heavy based saucepan over low heat. Add 1 tbsp of the butter and the olive oil, add onion and garlic and cook, without browning, until soft. Add the tomatoes. Add the rice and stir until all grains are coated with oil and have slightly warmed. Deglaze the saucepan with white wine then stir continuously until all liquid has been absorbed.
Add half the stock to the rice and stir to prevent rice sticking. When the liquid has reduced, add another quarter of the stock. When all liquid has been absorbed add remaining stock. Cook for a further 5 minutes until rice is cooked and creamy, add a little water if necessary.
For the crayfish, heat up a pan on med-high heat with butter and olive oil, add the crayfish meat, cook tossing until lightly coloured (about 3 min). Take of the heat, season with salt and pepper.
To finish the risotto, stir through the crayfish, basil, lemon juice and grated parmesan.
Divide the risotto onto each plate, top with a few extra pieces of crayfish, shaved parmesan, sprinkle with torn basil.