Preheat the oven to 350°F/175°C and line two large baking sheets with parchment paper or silicone baking mats. They spread less on parchment paper, so I'd recommend using that if you have it! Set aside.
In a large bowl, using a hand mixer or a stand mixer fitted with a paddle attachment, beat 1 cup of room temperature butter and 1 3/4 cups granulated sugar together at medium-high speed for a couple of minutes until it looks light and fluffy.
Add 1 large egg + 1 large egg yolk, 1 1/2 tsp peppermint extract (optional), and 1 tsp vanilla extract. Beat at a medium-high speed until combined. Scrape the sides and bottom of the bowl with a rubber spatula as needed.
Mix in 2 1/2 cups of flour, 1 Tbsp cornstarch, 1 tsp fine salt, and 1/2 tsp of baking soda on a low speed until mostly combined. Scrape the sides and bottom of the bowl with a rubber spatula, then increase the speed to medium and beat for a few more seconds to make sure all the ingredients are fully combined.
Split the batter into 2 equal portions (about 490g per bowl) and move one portion to a large bowl. Color one portion red with gel food coloring. You can start mixing the dough with a spatula, but eventually, you'll need to get in there and knead the dough with your hands. If you're worried about staining your hands, you can wear rubber gloves to do this. Mix until the dough is evenly colored.
Then use a teaspoon to scoop out teaspoon-sized portions of each dough. Roll each portion into a ball and set aside.
Next, take three portions of each color (you should have six little teaspoon-sized balls total) and place them in a small circle, alternating colors (red, white, red, white, etc.)
Use your fingers to press the different colors together to close the gap in the middle. Then cup your hand to round out the edges of the cookie. Gently use your forefinger to push the stripes of color in the same direction to give them a slightly swirled look.
Repeat with the remaining dough. You should end up with about 24 cookies. If desired, pour 1 cup of granulated or sanding sugar into a small bowl and toss the cookie dough in the sugar until it's fully coated. This adds a delicious bit of texture once the cookies are baked.
Chill the cookies in the fridge for 30 minutes or the freezer for 15 minutes, then place the cookies a few inches apart on the prepared baking sheets (they spread quite a bit!). I'd recommend only baking about 6 cookies on a tray at a time. Bake one tray at a time on the middle rack of your oven for 11-13 minutes, or until the edges look set but haven't started browning yet.
Remove the tray from the oven and let the cookies cool on the tray for 15 minutes, then move them to a wire rack to finish cooling. These can be stored in an airtight container at room temperature for up to 5 days.