Pecorino Romano's savory flavor enhances the mushroom's earthiness; sprinkling some over baked puff pastry before topping tarts keeps crust from getting soggy.
Preheat over to 400 degrees. On a lightly floured work surface, roll pastry to an 11-inch square, lightly score each square (do not cut all the way through), forming a 1-inch border. Using a fork, prick dough inside border.
Place pastry squares on baking sheet; refrigerate 10 minutes. Bake until golden, about 15 minutes.
Meanwhile, in a large skillet, heat oil over medium-high. Add mushrooms; season with salt and pepper. Cook, tossing frequently, until tender, 6 to 8 minutes.
Dividing evenly, sprinkle 1/2 cup Pecorino in center of baked pastry squares; top with mushrooms and remaining 1/4 cup cheese. Bake until cheese is melted and lightly browned, 6 to 8 minutes. Sprinkle with chives, and serve.