In a large bowl, or in a food processor or stand mixer, cream together the butter, cream cheese, and sugar until light and fluffy.
Add the egg and vanilla and cream until smooth.
Add the flour, baking powder, and salt and mix until well combined.
Divide the dough into 4 pieces (or however many colours you would like your cookies to be) and tint each a different colour. I find the fastest way to mix in the colour is with a food processor - add a few drops of gel food colouring and mix until it is well combined, adding more if you want the colour to be brighter.
Wrap each piece of coloured cookie dough tightly in plastic wrap and place it in the refrigerator to chill for at least an hour.
Preheat the oven to 350°F.
Divide each piece of cookie dough into two equal pieces.
Take one piece and roll it into an 8-10 inch log. Repeat with one piece of each of the other colours.
Press all four coloured logs together and roll to make one log of cookie dough that is multi-coloured. Slice this log into 12 equal pieces.
Roll each multi-coloured piece out into a snake, about 10 inches (35cm) long and twist it a bit to make the colours swirl around. Roll this up into a circle and place it on a cookie sheet.
Repeat with the remaining dough pieces, placing cookies about 2 inches apart on the cookie sheet.
Repeat steps #8-11 with the other half of the cookie dough pieces to make 12 more cookies.
Chill the cookies on the baking sheet for 15 minutes.
Bake the cookies for 9-10 minutes. Allow them to cool on the cookie sheet for 5 minutes before removing them to a rack to cool completely.
Store in an airtight container for 5-7 days at room temperature.