Preheat oven to 400°F. Sprinkle each puff pastry sheet with about 1/2 cup Parmesan, and gently press with a rolling pin to adhere. Cut each sheet into 9 (3-inch) squares. Gently press squares, cheese sides down, into 2 lightly greased (with cooking spray) 12-cup muffin pans. Place 1 teaspoon cream cheese into each tartlet. Chill, uncovered, while preparing mushrooms. 

Heat oil in a large skillet over medium-high. Add mushrooms; cook, stirring occasionally, until browned and tender, 8 to 10 minutes. Add Marsala, salt, thyme, and pepper. Cook, stirring often, until liquid has evaporated, about 1 minute. Remove from heat; cool slightly, about 15 minutes.

Divide mushrooms among tartlets. Sprinkle evenly with fontina. Bake in pre-heated oven until pastry is golden brown and cheese is melted, 18 to 22 minutes. Run a small offset spatula around each tartlet to loosen. Transfer to a wire rack. Garnish with thyme leaves; serve warm.