Preheat oven to 350°F. Line cookie sheets with parchment paper.
In a large bowl, cream together the butter and sugar until light and fluffy using a hand or stand mixer.
Mix in the vanilla and egg, scraping the sides of the bowl to fully incorporate.
Add the baking powder, salt, and half the flour. Mix on low speed, then scrape down the sides of the bowl. Add the remaining flour and mix until a soft dough forms.
Chill the dough in the refrigerator for 30 minutes.
Divide the dough into four equal portions. Leave one plain, and color the other three with pink, teal, and purple food coloring. (Tip: wear gloves and knead the color in by hand.)
To shape the cookies, take about ½ tablespoon from each dough color and roll them together into a ball. Don’t overmix—you want the colors to stay swirled and patchwork-like.
Gently flatten each ball with the bottom of a glass and place onto prepared cookie sheets.
Bake for 9–15 minutes, checking around the 9-minute mark. (Mine took about 14 minutes.) The cookies should be set but not browned.
Let cookies cool completely, then use black icing to pipe little “stitches” along the lines where the colors meet—just like Sally’s dress!