In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl or stand mixer, cream together the butter and sugar until light and fluffy, about 3-4 minutes.
Add eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.
Divide the dough into two equal portions. Add red food coloring to one portion, mixing thoroughly until the color is evenly distributed. Repeat with green food coloring for the second portion.
Place each colored dough between separate sheets of parchment paper. Roll each portion into a rectangle approximately 9x12 inches and ¼-inch thick.
Transfer both rolled dough sheets (still on parchment) to baking sheets and refrigerate for 15-20 minutes until slightly firm but still pliable.
Remove both dough sheets from the refrigerator. Peel off the top parchment from both colored doughs. Place the green dough (still on its bottom parchment) on your work surface.
Carefully flip the red dough onto the green dough, aiming to align the edges. Gently press the layers together and trim the edges to create a neat rectangle.
Starting from the long edge and using the bottom parchment as a guide, tightly roll the dough into a log. Wrap the log in plastic wrap and refrigerate for at least 2 hours or up to 3 days.
Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
Remove the dough log from the refrigerator, unwrap, and let stand for 5 minutes. Using a sharp knife, slice the log into ¼-inch thick rounds.
Place the slices about 2 inches apart on the prepared baking sheets. Bake for 10-12 minutes, until the edges are just beginning to turn golden.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.