Makes 24 hors d’oeuvres.
Brush the mushrooms caps with some of the reserved tomato oil and arrange them, stemmed sides down, on the rack of a broiler pan. Broil the mushrooms caps under a preheated broiler about 6 inches from the heat for 2 minutes, or until they are barely softened, and arrange them, stemmed sides up, in one layer on a baking sheet. In a large skillet cook the shallot and the garlic in the remaining reserved oil over moderately low heat, stirring occasionally, or until they are softened, stir in the reserved mushroom stems, the tomatoes, the thyme, and salt and pepper to taste, and cook the mixture, stirring occasionally, for 5 to 10 minutes, or until the liquid has evaporated and the mixture is thick. Stir in the cream and salt and pepper to taste, divide the mixture among the mushroom caps, and sprinkle it with the Parmesan. Bake the stuffed mushrooms in the middle of a preheated 350°F. oven for 12 to 18 minutes, or until the filling is heated through.