Step 1

Whisk the flour, baking powder and salt in a medium bowl. Beat the butter, granulated sugar and confectioners' sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 2 minutes. Beat in the egg yolks and vanilla until smooth. Reduce the mixer speed to medium low and gradually beat in the flour mixture until the dough just comes together.

Step 2

Divide the dough into 6 pieces: 2 large pieces (about 7 ounces each), 2 medium pieces (about 5 ounces each) and 2 small pieces (about 3 ounces each). Tint 1 large piece of dough red and the other orange, kneading the food coloring into the dough with gloved hands or a rubber spatula. Tint 1 medium piece of dough yellow and the other green. Tint 1 small piece of dough blue and the other purple.

Step 3

Using gloved hands, roll the purple dough into a 7-inch log (about 3/4-inch-thick) on a floured sheet of parchment paper; set aside. Using a rolling pin, roll out the remaining pieces of dough into rectangles on separate floured sheets of parchment paper, dusting with more flour as needed: 3 1/2 by 7 inches for blue; 5 by 7 1/2 inches for green; 6 by 8 inches for yellow; 7 by 8 1/2 inches for orange; 8 by 9 inches for red.

Step 4

Tightly wrap the blue dough around the purple log, keeping the dough in a log shape; pinch the seam to close. Continue wrapping the log with the dough: green, then yellow, orange and red. Wrap the whole log in plastic wrap; freeze until very firm, about 1 hour.

Step 5

Preheat the oven to 375 degrees F. Trim the ends of the dough log, then slice into 3/8-inch-thick rounds. Slice each round in half. Arrange about 1 inch apart on 2 unlined baking sheets and refrigerate until ready to bake, at least 15 minutes.

Step 6

Bake, one pan at a time, until the cookies are just set around the edges and golden on the bottom, 10 to 15 minutes. Let cool 5 minutes on the pan, then transfer to racks to cool completely.

Step 7

Meanwhile, put the candy melts in a medium microwave-safe bowl and microwave in 30-second intervals, stirring, until smooth, about 2 minutes. Transfer to a resealable plastic bag and snip a corner. Pipe small clouds on the ends of each rainbow. Let set, at least 5 minutes.