In large bowl, whisk together flour, baking powder and salt. Set aside.

In separate large bowl, using electric mixer on medium speed, beat butter with granulated sugar until creamy and light, about 3 minutes. Beat in egg and vanilla, scraping bottom and side, until combined.

Beat in half the flour mixture on low speed, then beat in remaining half.

Divide dough into quarters. Flatten each quarter into a disc, wrap in plastic wrap. Refrigerate until chilled, about 30 minutes.

Preheat oven to 375°F. Line 2 baking sheets with parchment paper; set aside.

On lightly floured work surface, roll out dough into ¼-inch thickness; using cookie cutters, cut into desired shapes. Arrange on prepared sheets.

Bake 1 sheet at a time until edges are pale golden, about 10 minutes. Let cool on rack.

Ice and decorate as desired.