Preheat oven to 275°. Beat butter at medium speed with a heavy-duty electric stand mixer until creamy; gradually add sugar, beating well. Stir in vanilla.
Stir together flour, ginger, and salt; gradually add to butter mixture, beating at low speed until blended after each addition.
Place dough on a lightly floured surface, and roll dough to 1/4 inch thick. Cut with a 2-inch round cutter. Place 2 inches apart on 2 parchment paper-lined baking sheets (about 12 per sheet). Reroll scraps once.
Bake, in batches, at 275° for 40 minutes or until lightly browned on bottom. (Refrigerate second batch while baking first batch.) Cool on baking sheet 2 minutes. Transfer to a wire rack, and cool completely (about 30 minutes).
Meanwhile, prepare Lemon-Cream Cheese Frosting. Spread about 1 Tbsp. on each cooled cookie, using a small spatula.