In a large bowl, whisk the first six ingredients until blended. Stir in bread, 1 cup cheese, ham and asparagus. Transfer to a greased 8-in. square baking dish. Refrigerate, covered, several hours or overnight. , Preheat oven to 325°. Remove strata from refrigerator while oven heats. Bake, uncovered, 20 minutes. Sprinkle with remaining cheese; bake 40-50 minutes longer or until puffed, golden and a knife inserted in the center comes out clean. Let stand 5-10 minutes before serving. Freeze option: After assembling, cover and freeze strata. To use, partially thaw in refrigerator overnight. Remove from refrigerator 30 minutes before baking. Preheat oven to 325°. Bake strata as directed, increasing time as necessary for a knife inserted in the center to come out clean.