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1
Melt 2 tablespoons butter in heavy large skillet over medium heat.
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2
Add shallots, tomatoes, garlic, basil, 2 teaspoons thyme and rosemary; saute 2 minutes.
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3
Add mushrooms; saute until very tender, about 15 minutes.
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4
Remove from heat.
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5
Season with salt and pepper.
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6
Cool.
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7
Preheat oven to 400F.
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8
Butter baking sheet.
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9
Melt 3 tablespoons butter in small saucepan.
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10
Place kitchen towel on work surface.
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11
Top with 1 phyllo sheet (keep remaining phyllo sheets covered with plastic wrap and damp towel).
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12
Brush with melted butter.
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13
Top with phyllo sheet; brush with butter.
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14
Sprinkle with 1/2 teaspoon thyme.
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15
Repeat layering with 2 more phyllo sheets, brushing with butter and sprinkling with remaining 1/2 teaspoon thyme.
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16
Top with another phyllo sheet; brush with butter.
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17
Starting 1 1/2 inches in from 1 long side and 2 inches in from each short side, spoon mushroom mixture onto phyllo in 2 1/2-inch-diameter log parallel to long sides.
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18
Fold short sides over filling; brush folded edges with butter.
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19
Using towel as aid and starting on long side nearer filling, roll up strudel jelly-roll style.
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20
Using spatula, transfer strudel to prepared baking sheet, seam side down.
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21
Brush strudel with butter.
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22
Freeze 5 minutes.
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23
Bake strudel until golden brown, about 15 minutes.
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24
Cut strudel into slices.
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25
Serve with Arugula Pesto.
