1. Whisk together flour, baking powder, and salt in a large bowl. With an electric mixer, cream butter with sugar 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, at least 20 minutes, or place in a resealable plastic bag and freeze up to 3 months (thaw in refrigerator overnight before using).

2. Preheat oven to 325 degrees. Line baking sheets with parchment. Remove one disk of dough; let stand 5 to 10 minutes, then roll it out 1/8 inch thick between two sheets of lightly floured parchment, dusting with more flour as needed. Cut out shapes with cookie cutters. Using a spatula, transfer to prepared baking sheets. (If dough gets soft, refrigerate 10 minutes.) Reroll scraps; cut more shapes. Repeat with remaining dough. Bake, rotating sheets halfway through, until edges are golden, 10 to 18 minutes (depending on size). Let cool completely on wire racks.

3. Place 1/2 cup buttercream in each of four small bowls. For the bright-pink color, add 1/4 teaspoon Berry food color. For the bright-red color, add 1/4 teaspoon Berry and 1/8 teaspoon Sunflower. For the bright-orange color, add 1/4 teaspoon Sunflower and a pinch of Berry. For the bright-yellow color, add 1/4 teaspoon Sunflower. Let stand 10 minutes before using to allow dyes to fully saturate.

4. Frost a few cookies using an offset spatula, then add a couple of tablespoons of white buttercream to each bowl to lighten the colors. Continue frosting cookies, then adding more white buttercream to achieve an ombre effect. Reserve remaining buttercream for another use.