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Preheat oven to 375 (if baking right away).
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Melt 2 T. butter in a saucepan and blend in flour.
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Cook over medium heat until smooth and bubbly, about 1 minute.
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Gradually add milk and cook until mixture boils and thickens, stirring constantly.
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Boil one minute.
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Add Swiss cheese and 2 T. parmesan, salt, cayenne and nutmeg.
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Stir until cheeses are melted and set aside.
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In medium skillet, brown sausage; drain.
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Stir in eggs and thyme and cook over medium heat until eggs are just set.
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Stir in cheese sauce and 1 T. parsley.
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Cool completely.
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Unroll phyllo and cover with plastic wrap or a damp cloth to keep moist.
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Brush one sheet with melted butter and sprinkle with bread crumbs.
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Fold in half lengthwise; brush with butter.
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Place 1/2 cup filling on bottom of short side of phyllo, leaving a one inch edge on bottom and sides. Roll up.
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Place seam side down on ungreased cookie sheet.
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In a small bowl, combine topping ingredients.
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Brush strudel with melted butter and sprinkle with topping.
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Repeat until all five strudels are made.
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Bake for 15 minutes or until crisp and light brown.
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These can be prepared, covered and refrigerated a day ahead, then baked as directed.