Put the mussels in a large nonreactive saucepan, cover tightly and bring to a boil over moderately high heat, stirring once in a while. (No liquid is needed; the mussels will release plenty of juices as they cook.) When all of the mussels have opened, after 8 to 10 minutes, remove the pan from the heat.
Transfer the mussels to a bowl. Strain the juices into a clean medium saucepan through a sieve lined with a moistened paper towel; you will have about 1 2/3 cups of mussel juices. Remove the meat from the shells. If you wish, pull of and discard the dark, frilly sinew that encircles each mussel.
To finish the sauce, add the onion, celery, scallions and garlic to the reserved mussel juices and boil gently for 10 minutes. Meanwhile, knead the butter and flour to a smooth paste. Whisk the paste into the boiling liquid. Add the parsley and simmer for 2 to 3 minutes, whisking until the sauce is smooth. Season to taste with salt and pepper.
Melt the butter in a medium saucepan. Add the onion and thyme, mix well and cook over moderately high heat for 1 minute. Add the rice and stir to coat the grains with butter. Add the water and salt and bring to a boil, stirring. Reduce the heat to very low, cover the pan and cook for 20 minutes.
Generously butter four 1 1/4-cup custard dishes, bowls or ramekins. Reheat the mussel sauce and add the cooked mussels to it.
Spoon 1/2 cup of the hot rice pilaf into each custard dish. Press the rice against the side of the dish with a spoon to make a nest in the center. Spoon 10 mussels and 3 tablespoons of their sauce into each nest and cover with another 1/2 cup of rice pilaf. Press on the rice with the back of a spoon to pack it down slightly. Invert the molded mussel pilafs onto warmed serving plates; they will slide out easily. Spoon the remaining mussels and sauce around the pilafs and serve at once.