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 of 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.
Freeze option: After topping strudels with cheese and parsley, freeze unbaked on a waxed paper-lined baking sheet until firm. Transfer to a freezer container; return to freezer. To use, bake strudels as directed, increasing time to 30-35 minutes or until heated through and golden brown.