These crispy, flaky ham and cheese breakfast strudels are filled with creamy scrambled eggs, savory ham, Swiss cheese, and Parmesan. They're easy to make ahead and can be frozen unbaked for a convenient freezer-friendly breakfast.
In a small saucepan, melt 2 tablespoons butter. Stir in flour until smooth; gradually add milk. Bring to a boil; cook and stir 2 minutes or until thickened. Stir in cheeses and salt.
In a large nonstick skillet, melt remaining 1 tablespoon butter over medium heat. Add eggs to pan; cook and stir until almost set. Stir in ham and the cheese sauce; heat through. Remove from heat.
Preheat oven to 375°. Place 1 sheet phyllo dough on a work surface. Keep remaining phyllo covered with a damp towel to prevent it from drying out. Brush with melted butter; sprinkle with 2 teaspoons bread crumbs. Fold phyllo in half lengthwise; brush again with butter. Spoon 1/2 cup filling onto phyllo about 2 in. from a short side. Fold side and edges over filling and roll up. Brush with butter. Repeat with remaining phyllo, butter, bread crumbs and filling.
Place on a greased baking sheet; sprinkle each with 1 teaspoon cheese and 1 teaspoon parsley. Bake 10-15 minutes or until golden brown. Serve immediately.