To make the cookie dough:
In a bowl, whisk together the flour, baking powder and salt.
In the bowl of a stand mixer cream together the butter and sugar with the paddle attachment, until light and fluffy, about 2 minutes on medium-high speed. Scrape down the sides of the bowl. Add the eggs one at a time, mixing well between each and scraping the sides of the bowl. Mix in the vanilla and flavored extracts. Add the flour all at once and mix on low speed just until it all comes together. Scrape down the bowl and turn the speed to medium, beat for 15 seconds.
Divide the cookie dough into 3 bowls (or more if you are adding additional colors). Add paste or gel food coloring to achieve the color you want.
Wrap the colored dough in plastic and refrigerate until set up, at least an hour.
Line a container with plastic wrap. Pick one that is tall enough to get several layers of the cookie dough and will hold all of the dough you prepared.
There are two ways to get the dough into the prepared container. You can simply press the dough into the container, which will result in random thicknesses or
You can roll the colored dough out on a floured surface...
and cut out the thin layers to place into the container. Rolling the dough out results in very even stripes.
Once you have used up your dough, wrap the filled container and refrigerate for several hours. A well-chilled dough is key for getting even slices. You can also freeze the dough at this point for up to a month.
To bake the cookies:
Preheat oven to 350 degrees F. Line cookie sheets with parchment.
Once the dough is thoroughly chilled, and defrosted, if frozen, unwrap the dough and use a very sharp, thin blade knife to cut even slices of dough. Try to get 1/8-inch-thick slices, but the most important thing is to cut the dough evenly. All of the cookies should be the same thickness.
Use a cookie cutter to create fun shapes out of the dough. Place the cut cookies on a cookie sheet lined with parchment paper. If your dough starts to get warm and sticky, return it to the refrigerator. Warm dough will make it more difficult to cut and work with.
If you want to make larger cookies, you can place two slices of the cookie dough next to each other on a sheet of parchment to create a larger piece of dough. Refrigerate the dough to get it well chilled before using the large cutter.
Use a large cookie cutter to make your shapes. Smaller cutters are good for using up the dough around the large shape, so there is as little waste as possible.
Only bake same-size cookies on a sheet, so they bake evenly. Bake for 5 minutes, then rotate the tray front to back and top to bottom, if you are baking more than one tray at a time. Continue baking until just barely golden on the bottom, about 3 to 5 minutes.
Cool the cookies on a rack. Serve them at a party or pack them up as gifts.