Preheat oven to 450 degrees F. In a medium bowl stir together flour, basil, cayenne pepper, and salt. Cut in shortening until pieces are pea-size. Sprinkle 1 tablespoon of the water over part of the flour mixture; gently toss with a fork. Push moistened dough to side of bowl. Repeat, using 1 tablespoon water at a time, until flour mixture is moistened; form into a ball. On a lightly floured surface, slightly flatten dough.
Roll dough from center to edges into a 12x12-inch square. Cut pastry square into four 6-inch squares. Ease pastry squares into four jumbo muffin cups, pleating sides to fit. Generously prick bottom and sides of pastry with a fork.
Bake for 5 to 8 minutes or until just beginning to brown. Meanwhile, in another medium bowl combine tomatoes, red onion, and vinaigrette. Mix to coat tomatoes; spoon tomato mixture into prebaked cups; drizzle any remaining vinaigrette over the tomatoes. Sprinkle with grated cheese, if desired. Bake 10 minutes more or until heated through and tomatoes just begin to give up their juices. Cool at least 15 minutes on a wire rack. Makes 4 servings.