Beat butter and 1 cup sugar at medium speed with an electric mixer until creamy. Add egg and vanilla; beat 30 seconds. Add flour, beating at low speed until combined.

Place dough on lightly floured parchment paper, and roll to 1/4-inch thickness. Transfer rolled dough and parchment paper to a baking sheet, and chill 15 minutes.

Preheat oven to 375°. Cut dough with lightly floured 2-inch cutters; place 1/2 inch apart on 2 parchment paper-lined baking sheets. Reroll scraps, and repeat process.

Bake, in batches, at 375° for 8 to 10 minutes or until golden brown around edges. Cool completely on a wire rack (about 30 minutes).

Whisk together 2 1/2 Tbsp. water and remaining 2 cups powdered sugar. Dip top of each cookie in glaze, and transfer to a wire rack in a jelly-roll pan. Sprinkle with nonpareils. Let stand 1 hour or until set.