Preheat oven to 400 degrees. Cut tops off tomatoes, and reserve. Remove and discard seeds; salt flesh. Drain upside down on a rack set over a baking sheet. Meanwhile, roll out puff pastry to a 13-by-12-inch rectangle; cut into 6 pieces. Press into cups of a standard muffin tin, overhanging sides. Cover with plastic wrap; set aside.
Heat oil in a nonstick skillet over medium-high heat until hot but not smoking. Add onion and celery; cook until onion is golden, 3 minutes. Add sausage; cook, stirring occasionally, until browned, 10 minutes. Remove from heat; stir in parsley and cheese.
Divide sausage mixture among tomatoes; place 1 in each pastry shell. Lightly beat egg with cream; brush onto edges of shells. Turn corners of pastry up around tomato slightly.
Bake until pastry is golden, 15 minutes; return tomato tops halfway through baking. Let rest 10 minutes before serving.