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1
Prepare two rimmed baking sheets, coated with cooking spray.
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2
Line a large baking sheet (approximately 12 by 17 inches) with parchment paper.
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3
Lay one large sheet of phyllo on the prepared pan.
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4
Keep the remaining phyllo covered with wax paper or plastic wrap and a damp kitchen towel.
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5
Lightly brush oil on the phyllo sheet evenly with a pastry brush or you can use cooking spray.
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6
Sprinkle with 1 teaspoon breadcrumbs.
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7
Repeat the same step, and go on layering the remaining phyllo on top.
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8
Carefully roll about 3/4 inch of each side toward the center to form the outer rim of the tart.
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9
Cut into 4 squares.
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10
Arrange squares on 2 rimmed baking sheets.
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11
Heat oil in heavy large skillet over medium-high heat.
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12
Add mushrooms, sprinkle with 1/4 teaspoon coarse salt and 1/4 teaspoon pepper.
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13
Saute until tender and lightly browned, about 4 minutes.
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14
Transfer mushrooms to large bowl; cool 15 minutes.
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15
Add asparagus, chopped thyme, lemon peel, 3/4 teaspoon coarse salt, and 1/4 teaspoon pepper to mushrooms.
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16
Mix in creme fraiche and cheese.
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17
Do ahead: Filling can be made 1 day ahead.
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18
Cover; chill.
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19
Position 1 rack in top third and 1 rack in bottom third of oven and preheat to 400F.
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20
Mound filling atop pastry squares, leaving 1/2-inch plain border.
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21
Bake tarts 12 minutes.
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22
Reverse sheets.
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23
Continue to bake tarts until crusts are puffed and golden and filling is cooked through, about 10 minutes or longer.
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24
Transfer to plates; garnish with thyme sprigs.
