Stir together flour, and baking powder in a bowl.
Beat together butter, granulated sugar, cream cheese, and salt in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 5 minutes. Add vanilla extract and beat until incorporated.
Reduce the speed of the electric mixer to low and add flour mixture in 3 batches, mixing until dough just comes together in clumps.
Place dough on a lightly floured surface. Gather and press dough together with your hands. Then divide into 3 equal pieces (326 g each piece).
Shape one piece of the dough into a disk and wrap it securely in plastic wrap. This will be the white layer.
Return one of the pieces of dough to a mixing bowl, and with the mixer on "low," add in the red food coloring until it reaches your desired color. Remove from bowl, shape into a disk, and wrap it securely in plastic wrap.
Add the final piece of dough to a mixing bowl, and with the mixer on "low," add in the green food coloring until it reaches your desired color. Remove from bowl, shape into a disk, and wrap it securely in plastic wrap.
Refrigerate all 3 disks for 1 hour. Remove the dough from the fridge. On a lightly floured surface roll out each disk into a 4 x 6 inches rectangle.
Starting with the white dough as the base, stack the rectangles on top of one another. Run the rolling pin over the stack a few times to make sure everything is even. Then keep rolling to create a rectangle of 13 x 10 inches.
Starting from the long side, roll up the dough stack tightly to create a log. Cut the log into 3 pieces. Roll each log in coarse sugar, coating it evenly, if desired. Wrap logs with plastic wrap. Refrigerate for at least 2 hours up to a month.
Position two oven racks, evenly spaced, in the middle of the oven. Preheat the oven to 350º F (180º C) and line two baking sheets with parchment paper.
Using a sharp knife, cut the log into ¼ inch thick slices. Arrange slices on the prepared baking sheets, spacing them evenly. Keep the remaining logs in the refrigerator until the first batch bakes.
Bake for 13 – 14 minutes, or until slightly puffy and the edges look set. Let them cool in the baking sheets for 5 minutes and then transfer cookies to a wire rack to cool completely. Let the baking sheets to cool and then bake the remaining cookies.