Preparation Roll out each pastry sheet on work surface to 10-inch square. Cut each into 4 squares. Using small knife, score 1/2-inch border (do not cut through pastry) around inside edges of each square. Arrange squares on 2 rimmed baking sheets. DO AHEAD: Can be made 1 day ahead. Cover and chill. Melt butter in heavy large skillet over medium-high heat. Add mushrooms; sprinkle with 1/4 teaspoon coarse salt and 1/4 teaspoon pepper. Sauté until tender and lightly browned, about 4 minutes. Transfer mushrooms to large bowl; cool 15 minutes. Add asparagus, chopped thyme, lemon peel, 3/4 teaspoon coarse salt, and 1/4 teaspoon pepper to mushrooms. Mix in crème fraîche and cheese. DO AHEAD: Filling can be made 1 day ahead. Cover; chill. Position 1 rack in top third and 1 rack in bottom third of oven and preheat to 400°F. Mound filling atop pastry squares, leaving 1/2-inch plain border. Bake tarts 12 minutes. Reverse sheets. Continue to bake tarts until crusts are puffed and golden and filling is cooked through, about 10 minutes longer. Transfer to plates; garnish with thyme sprigs. Sold at most supermarkets and at specialty foods stores.
Preparation Roll out each pastry sheet on work surface to 10-inch square. Cut each into 4 squares. Using small knife, score 1/2-inch border (do not cut through pastry) around inside edges of each square. Arrange squares on 2 rimmed baking sheets. DO AHEAD: Can be made 1 day ahead. Cover and chill. Melt butter in heavy large skillet over medium-high heat. Add mushrooms; sprinkle with 1/4 teaspoon coarse salt and 1/4 teaspoon pepper. Sauté until tender and lightly browned, about 4 minutes. Transfer mushrooms to large bowl; cool 15 minutes. Add asparagus, chopped thyme, lemon peel, 3/4 teaspoon coarse salt, and 1/4 teaspoon pepper to mushrooms. Mix in crème fraîche and cheese. DO AHEAD: Filling can be made 1 day ahead. Cover; chill. Position 1 rack in top third and 1 rack in bottom third of oven and preheat to 400°F. Mound filling atop pastry squares, leaving 1/2-inch plain border. Bake tarts 12 minutes. Reverse sheets. Continue to bake tarts until crusts are puffed and golden and filling is cooked through, about 10 minutes longer. Transfer to plates; garnish with thyme sprigs. Sold at most supermarkets and at specialty foods stores.