End-of-the-Rainbow Cookies

In a medium bowl, whisk together flour, baking powder, and salt. Beat butter and granulated sugar on medium-high speed until light and fluffy. Beat in egg and vanilla until combined. Reduce speed to low and add flour mixture, beating until just combined.

Divide dough in half. Divide one half into 2 pieces (about 3/4 cup each). Flatten one piece into a 3-by-5-inch rectangle; wrap tightly with plastic. Roll out other piece into an 8-inch rod shape, about 1 inch thick; wrap tightly with plastic. Divide remaining half of dough into 3 pieces (about 1/2 cup each), then tint each with one of the gel colors, stirring color in with a spatula. Flatten each tinted piece into a 3-by-5-inch rectangle; wrap each tightly with plastic. Refrigerate all dough until firm, at least 1 hour and up to 2 days.

In a small bowl, whisk egg white with a fork. On a lightly floured work surface, roll out turquoise dough into a 4-by-8-inch rectangle, about 1/4 inch thick. Brush with egg white. Place dough rod on long edge of rolled-out dough, then roll rod inside it; seal at edges where dough meets by pinching and pressing gently. Freeze 10 minutes. Repeat with remaining dough, rolling yellow dough out to 5 by 8 inches, pink dough to 6 by 8 inches (1/8 inch thick), and untinted dough to 7 by 8 inches. Roll log in plastic wrap; twist ends closed. Refrigerate until very firm, at least 2 hours and up to 1 month.

Preheat oven to 350 degrees. Let dough stand at room temperature about 10 minutes; remove plastic wrap. Line baking sheets with parchment paper. Using a sharp chef's knife, slice log into 1/4 inch-thick rounds, rotating log after each cut to keep it round. Transfer rounds to sheets and bake until set and just golden around edges, 15 to 17 minutes. Transfer sheets to wire racks and cut each cookie in half with a sharp knife to form two rainbows. Let cool completely.

In a small bowl, stir 1 to 2 teaspoons water into confectioners' sugar until mixture is thick and smooth. Use to adhere halved peanut-butter cups and gold sequins to cookies; let stand until glaze hardens, 30 minutes. Sprinkle with gold stars. Cookies can be stored in an airtight container at room temperature up to 5 days.