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1
Preheat oven to 350F (180C).
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2
Heat half the oil in a large skillet over medium-high heat, add shallots and saute for 60 seconds.
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3
Add the mushrooms and 1/4 teaspoon of salt and saute for 10 to 12 minutes or until most of the moisture has evaporated.
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4
Mix in asparagus and saute until slightly tender, about 2 or 3 minutes.
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5
Cool slightly, then mix in the parsley, lemon zest, lemon juice, pepper and 3 tablespoons of Parmesan cheese.
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6
Mix well, taste and adjust seasoning if needed and set aside.
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7
Working on a clean surface, brush the first sheet of phyllo with olive oil and sprinkle with 1/4 teaspoon of thyme.
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8
Repeat with remaining phyllo sheets, stacking one top of the other with the longer sides parallel to the counter's edge.
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9
Place filling along the longer edge of phyllo and roll into a log, tucking in the sides to prevent mixture from falling out.
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10
Carefully place on a baking sheet that has been sprayed with cooking spray or line with parchment paper.
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11
Brush strudel with olive oil and top with Parmesan cheese
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12
Cut three diagonal slits width-wise into top of strudel.
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13
Bake for about 17 minutes or until golden brown.
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14
Cool slightly.
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15
Slice where strudel is slit to make four equal portions.
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16
Serve warm.
