Beat cold butter and sugar on medium speed for 2 minutes until sandy. Add cold cream cheese and beat 1 minute until fluffy. Mix in the cold egg and vanilla until just combined.

Whisk flour, baking powder, and salt together. Add to the butter mixture on low speed until the dough comes together.

Divide the dough into five equal pieces. Color them red, orange, yellow, green, and blue using gel coloring, kneading gently until the color is even.

Pinch off small pieces of each color, stack them, and roll into a ball. Roll between parchment sheets to 1/4 inch thick and cut with a floured cutter. Place on a parchment lined baking sheet.

Preheat oven to 350°F (175°C). Bake for 10 to 12 minutes until edges are set but centers are pale. Cool on the sheet for 5 minutes.

Transfer to a wire rack to cool completely, then serve.