Heat oven to 375 degrees. Melt 2 tablespoons butter in small saucepan. Blend in flour, cook over medium heat until smooth and bubbly, about 1 minute. Gradually add milk; cook until mixture boils and thickens, stirring constantly. Boil 1 minute. Add Swiss and parmesan cheeses, salt, cayenne pepper, and nutmeg. Stir until cheeses are melted. Set aside. In medium skillet, brown sausage, drain. Stir in eggs and thyme. Cook over medium heat until eggs are just set. Stir in cheese sauce and 1 tablespoon parsley. Cool completely.
Unroll phyllo sheets: cover with plastic wrap or towel. Brush 1 phyllo sheet with melted butter, sprinkle with bread crumbs. Fold in half lengthwise, brush with butter. Place 1/2 cup filling on bottom of short side of phyllo, leaving 1 inch edge on bottom and sides. Turn up edge. Fold in sides. Roll up. Place seam side down on ungreased cookie sheet.
In small bowl, combine topping ingredients. Brush strudel with melted butter; sprinkle with topping. Repeat with remaining phyllo sheets. filling, and topping. Bake at 375 for 15 minutes or until crisp and light brown. Serves 5 -can easily double.
Note: Strudels can be prepared, covered, and refrigerated a day ahead, then baked as directed.