Serves 6 or more, about 36 1 ½ inch ravioli
Separate the lobster meat from the shells. The meat will be used in the ravioli filling, the shells to flavor the sauce.
Make lobster sauce first. In a large saucepan or stock pot, melt the butter and the olive oil together over medium heat. Add the carrot, onion, celery, bay leaf and garlic. Cook 1-2 minutes until aromatic. Add the lobster shells and continue to sauté, stirring regularly for 10-15 minutes until the vegetables are tender and light brown. Pour on the brandy, stirring to dislodge any brown bits from the bottom of the pan. Simmer for 3 minutes, or until the liquid is reduced by half.
Add the chicken stock, bring the stock to a boil then reduce the heat and simmer with the lid slightly ajar for 1 hour. Strain the stock through a sieve. Discard the solids and pour the strained stock into a saucepan. Add the cream. Bring the sauce to a boil and cook over medium high heat until the sauce is glossy and thickened, about 30 minutes. Season to taste with salt and pepper, noting that the sauce may already be quite salty from the lobster shells
While the sauce is simmering, make the lobster filling. In a medium saucepan, combine the cream and brandy. Boil over medium high heat until it has reduced by half to a syrupy consistency, 3-4 minutes. Chop up the lobster meat and stir into the warm cream. Season with salt and pepper. Place lobster and cream mixture in a blender or food processor with the egg white and puree to a smooth, thick paste. Chill until ready to use.
To make the ravioli, lay one sheet of pasta flat onto a well-floured work surface. Spoon 1 teaspoon of the lobster filling in intervals of 2 inches. (Each spoonful of filling will be a ravioli, so make sure there is enough room to form and seal the pasta.) Using a small brush, brush the egg yolk and water mixture lightly around the spoonfuls of ravioli filling. Place another pasta sheet on top of everything and gently press down with your fingers. Try to eliminate excess air in the ravioli or they may burst during cooking. Press more firmly to seal the layers, then cut the pasta with a wheel to make the desired ravioli shape. Pull the pieces apart and dust generously with flour. Place finished ravioli on a baking sheet or tray generously dusted with additional flour. Repeat with the remaining ingredients. Chill ravioli until ready to cook.
Bring a large pot of salted water to a boil. Cook the ravioli in the water until al dente, 2-3 minutes. Drain well and place the cooked ravioli onto individual plates. Spoon the warm lobster sauce on top and garnish with diced tomatoes and basil.