Preheat oven to 375°.
To prepare cookies, lightly spoon flour into dry measuring cups; level with a knife. Combine flour, cornstarch, and salt in a medium bowl, stirring well with a whisk.
Combine 1 cup powdered sugar, butter, cheese, and vanilla in a large bowl; beat with a mixer at medium speed until light and fluffy (about 4 minutes). Add flour mixture; stir until just combined (dough will be dry and crumbly). Shape dough into 36 (1-inch) balls. Place balls 2 inches apart on baking sheets. Bake at 375° for 10 minutes or until bottoms of cookies are lightly browned. Cool 5 minutes on pans on wire racks. Remove from pans; cool completely on wire racks.
To prepare glaze, combine 1 3/4 cups powdered sugar and lemon juice, stirring with a whisk until smooth. Dip tops of cookies in glaze; place on wire racks. Let cookies stand for 30 minutes or until glaze is set.