Step 1: Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper.
Step 2: In a large bowl, cream together the softened unsalted butter and granulated sugar until light and fluffy (about 2-3 minutes).
Step 3: Beat in the egg yolk and 1 teaspoon of vanilla extract until well combined.
Step 4: In a separate medium bowl, whisk together the all-purpose flour, baking powder, and 1/4 teaspoon salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and a dough forms.
Step 5: Divide the dough in half. On a lightly floured surface or between two sheets of parchment paper, roll each half to about 1/8-inch thickness. Chill the rolled dough in the refrigerator for at least 30 minutes.
Step 6: Using a small cookie cutter (approx. 1.5 inches, like a circle or animal shape), cut out the cookies. Place them on the prepared baking sheets, leaving a small space between each cookie. Re-roll any dough scraps as needed.
Step 7: Bake for 8-10 minutes, or until the edges are lightly golden. Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.
Step 8: While the cookies cool, prepare the frosting. In a medium bowl, beat the softened cream cheese until smooth and creamy.
Step 9: Gradually add the powdered sugar to the cream cheese, beating until fully incorporated and smooth. Start on low speed to prevent sugar from flying.
Step 10: Beat in 1 teaspoon of vanilla extract and a pinch of salt until well combined.
Step 11: Gently fold in the rainbow sprinkles until evenly distributed. Avoid overmixing to prevent the colors from bleeding.
Step 12: Serve the cooled cookies with the sprinkle frosting for dipping. Store leftover cookies in an airtight container at room temperature for up to 3-4 days, and the frosting in an airtight container in the refrigerator for up to a week. Let frosting come to room temperature before serving.