Beat the butter and sugar on medium-high speed until the sugar is dissolved and creamy.
Add the eggs and flavored extract to the butter and beat until all ingredients are well incorporated. Then, in a small glass dish, dissolve the baking soda in 4 tablespoons of milk and add to the mixture, beating until combined.
Finally, add the salt followed by the flour 1 cup at a time, then 2 tablespoons of milk, and mix until a stiff dough forms.
Divide the dough into 3 equal-sized balls. Dye one red, and one green and leave one undyed using either your mixer or your hands (see notes for additional tips). Then divide each ball in half (it’s easier to work with smaller portions)
Starting with the red, roll each individual color into a rectangular shape, about 10 inches long and 6 inches wide, and ¼ inch thick. Roll between two pieces of parchment paper and lightly dust with flour if needed to prevent sticking.
Proceed to roll out the undyed color, and then place it directly on top of the red. It’s helpful to use a rolling pin to transfer the dough. Next, do the green.
Once all the colors are stacked, cover with a second piece of parchment paper and proceed to roll out the cookie dough again until it’s about ⅜ inch thick. Trim off the excess sides with a knife or pizza cutter.
Starting with the narrow edge, roll tightly into a log. Once rolled, use your hands to roll again, to expand the log. Wrap tightly with plastic wrap and place seam side down and chill for at least 30-60 minutes.
Preheat oven to 350°F. Line a baking sheet with a silicone baking mat.
Remove the dough from the fridge. Using a sharp knife, cut them into ⅜-inch wide slices. If they are misshaped, gently roll them between your hands to shape them into a circle. Place about 1-inch apart on the baking sheet.
Bake at 350° for 9-11 minutes just until the bottoms turn slightly brown. Allow to cool for 5 minutes before transferring to a wire rack to cool completely.
