Cookies: In a bowl, whisk together flour, baking powder, and salt. Beat butter and sugar on medium-high speed until light and fluffy. Beat in egg and vanilla. Reduce speed to low and gradually add flour mixture; beat until combined. Divide dough in half; flatten into disks. Wrap each in plastic and freeze until firm, about 20 minutes.

Preheat oven to 325 degrees. Line 2 rimmed baking sheets with parchment. Remove 1 disk of dough; let stand 5 to 10 minutes. Roll out 1/8 inch thick between two sheets of floured parchment, dusting with flour as needed. Cut shapes with 2 1/2-inch heart-shaped cookie cutters. Using a spatula, transfer to prepared baking sheets (if dough gets too soft, refrigerate 10 minutes). Reroll scraps and cut more shapes. Repeat with remaining disk of dough.

Bake cookies, rotating sheets halfway through, until edges are golden, about 12 minutes. (If bubbles form, tap baking sheet firmly against oven rack a few times during baking.) Let cool completely on wire racks. Cookies can be stored in an airtight container up to 1 week.

Royal Icing: In the bowl of a mixer fitted with the paddle attachment, combine confectioners’ sugar and egg white on low speed. Add a scant 1/4 cup water, then increase speed to medium-high and mix until icing holds a ribbon-like trail on surface for 3 seconds when you raise paddle, about 10 minutes. Reduce speed to low and mix 1 minute more to eliminate air bubbles. Add food color, a drop at a time, until desired color is reached. Use immediately, or store in an airtight container in refrigerator up to 3 days. Stir well before using. Decorate cookies as desired.