Preheat the oven to 375 degrees F. Spray a baking sheet with vegetable oil cooking spray. Remove the puff pastry from the freezer and allow it to thaw for 20 minutes.
Unfold the pastry on the counter and roll down, using enough flour to prevent sticking. Brush the dough with olive oil and, using a 1 1/2- or 2-inch biscuit cutter, cut out rounds of dough. Place the puff pastry rounds on the prepared baking sheet and poke the surface of the pastry with a fork. Top each round with a small amount of the Cheddar, then with a tomato slice. Sprinkle salt and pepper to taste over the tomato, and then sprinkle on a pinch of thyme and about 1 teaspoon of Parmesan. Bake for about 15 minutes. Let cool for 2 to 3 minutes before serving.