Rinse the mussels under cold running water, rubbing the shells against each other to remove any encrustation. Remove the beards with a knife. Rinse the mussels well again under cold water and discard any mussels that seem unusually heavy.

In a large stockpot, place the large onion, celery, 2 of the garlic cloves, bruised, the parsley sprigs, thyme, pepper to taste, and wine. Bring to a boil, lower the heat, and simmer, covered, for 15 minutes.

Raise the heat to moderately high and when the wine is boiling add all the mussels. Cover and cook until the mussels have opened, about 5 minutes, shaking the pot a couple of times.

Remove the mussels from the pot with a pair of tongs and place them in a large bowl. Then lift the mussels out of their shells, place them in a bowl, and set aside. Discard any mussels that have not opened.

Strain the cooking liquid through a sieve lined with several layers of cheesecloth into a bowl. Pour 3 tablespoons of the strained liquid over the reserved mussels and cover the bowl with plastic wrap. Pour the rest of the liquid into a small stainless steel saucepan and reduce the liquid over high heat until only 1/4 cup remains.

In a small skillet, heat the butter over moderately low heat and in it cook the finely chopped onion until tender but not browned. Add the remaining garlic clove, minced, and the chopped tomatoes and cook, stirring, for 1 minute. Add the reduced cooking liquid and the cream, raise the heat to moderate, and boil gently until the sauce has thickened slightly, about 5 minutes. Turn off the heat. Lift the mussels out of the bowl, leaving the liquid behind, and place them in the cream sauce.

In a kettle, bring 5 quarts water to a boil and add the salt and vegetable oil. Add the linguine, stir, and cook until al dente. Drain thoroughly.

While the pasta is cooking, heat the sauce and mussels very gently.

In a large bowl toss the pasta with the sauce and the chopped fresh basil. Serve in heated bowls.