For the stock: Combine the tomato, garlic, peppers, carrots, chili pepper, parsley, bay leaf and peppercorns in a large stock pot and cover with 2 quarts of water. Bring to a boil over high heat, then lower the heat to a simmer.
Using a sharp knife, separate the lobster head from the claws and body. Refrigerate the body until ready to use in the paella. Heat 1 tablespoon of olive oil in a large sauté pan over medium-high heat, add the lobster head, claws and the crabs and cook until they turn red. Add the lobster head and crabs to the stockpot and continue to simmer the stock for 1 hour.
Remove the stock from the heat. Transfer the lobster head, the crabs and 2 cups of the stock to a blender and puree. Set a fine mesh strainer over the stockpot and pour the puree through the strainer back into the pot and stir until well combined. Then strain all of the stock through another fine mesh strainer or a cheesecloth-lined colander. Set the stock aside and discard the solids.
Prepare the rice: Using a sharp knife, cut up the reserved lobster. Separate the claws from the knuckles and slice the tail into 4 pieces. Crack the claws with the knife so they will be easy to pull apart once they are cooked. Cut the knuckles into 2 pieces.
In a 13-inch paella pan, heat 2 tablespoons of the olive oil over medium heat for 2 minutes until just smoking. Add the lobster pieces and sauté about 1 minute on each side. Transfer the lobster to a plate. Pour 2 more tablespoons of the olive oil into the paella pan, then add the chanterelles and sauté for 2 minutes.
Stir in the rice and salmorra and cook for 1 minute. Pour in 4 cups of the strained stock and stir until well combined, about 30 seconds. Increase the heat to high and cook for 6 minutes. Do not stir the rice again as it may cause the rice to cook unevenly.
Add the saffron and season to taste with salt. Reduce the heat to low and simmer for 11 minutes. After about 6 minutes, add the lobster pieces to the paella to continue to cook for the final 5 minutes. The rice should have absorbed all of the liquid. Remove the paella from the heat, cover with a clean kitchen towel and let the paella rest for 5 minutes before serving. Serve with spoonfuls of allioli.
For the Salmorra: Heat the oil in a medium pot over medium heat. Add garlic and sauté until soft, about 2 minutes. Add the chili peppers and toast, stirring, for about 3 minutes, then add the tomatoes and sugar. Cook for 15 minutes or until the tomato liquid evaporates. Stir in the pimentón. Transfer the mixture to a blender and purée. Pour into a bowl, and season to taste with salt. Makes 2 cups.
José’s tips: This sauce can be kept in the refrigerator, covered, for up to two weeks or frozen for up to 3 months. Be sure to drizzle the top of the sauce with some olive oil before you cover it to prevent it from drying out.