In a large mixing bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat together the butter, brown sugar, and sugar on high speed for 1 minute or until smooth and creamy. Add in the eggs, milk, vanilla, and butter extract. Beat together for 30 seconds. Add in the flour mixture and bring together until fully incorporated.
Divide the dough in half and place each half in a separate bowl. Add red food coloring and vanilla extract to one bowl and green food coloring and butter extract to the other bowl. Mix well until the cookie dough in each bowl is evenly colored.
Transfer each dough ball onto its own large piece of plastic wrap. Shape each ball of dough into a 5-inch x 5-inch square. Wrap tightly with plastic wrap and place both squares into the fridge to chill for 30 minutes.
Once the dough has chilled, remove the plastic wrap, and stack the dough squares on top of each other so that they are aligned. Place the dough onto a lightly floured surface. Gently flour the top of the dough. Use a rolling pin to roll the square out into a rectangle about 9 inches wide and 18 to 20 inches long. Roll the dough up into a log. Tightly wrap the log with plastic wrap and place it into the fridge to chill for at least 1 hour.
Once the dough log has chilled, preheat your oven to 350 degrees F and line a baking sheet with parchment paper.
Unwrap the plastic wrap from around the dough log. Place the log onto a cutting board and slice it into ½-inch thick cookies. (If needed cut a thin slice from the ends of the log first, so they are even.) You should have about 18 cookies. Place the cookies onto the prepared baking sheet leaving at least 3 inches of space between each cookie as they will spread.
Bake for 18-20 minutes. The cookies should not be browned around the edges. The edges will feel set and the rest of the cookie will feel soft.
Remove the baking sheet from the oven and place the cookies onto a wire rack to cool completely. Allow the cookies to cool for at least 10 minutes before serving, as this allows the cookies to set up.
Notes
If you don't have unsalted butter on hand, skip adding salt to the dry ingredients and use salted butter instead.
You could swap out the butter extract for more vanilla extract, almond extract, or peppermint extract if desired.
For a more vibrant color, use gel food coloring instead of liquid food color.
You can store the baked cookies in an airtight container on the counter for up to 5 days.
The cookie dough can be frozen once formed into a log and wrapped tightly with plastic wrap. When you're ready to bake, let the dough thaw for 15-20 minutes or until you can easily slice through it. Then slice and bake as instructed in the recipe.