Stir together cream cheese and butter until blended; stir in 3/4 cup flour and cornmeal. Cover and chill 1 hour.
Shape dough into 18 (1-inch) balls. Place balls into miniature muffin pans, and press evenly into bottom and up sides. Set aside.
Stir together Swiss cheese and 1 tablespoon flour.
Whisk together egg and whipping cream; stir in Swiss cheese mixture and diced ham. Spoon evenly into pastry shells.
Bake at 425° for 7 minutes. Top each tart with an asparagus spear. Reduce oven temperature to 300°. Cover and bake 17 minutes or until set.
