Prepare the vanilla cookie dough first. Start by putting the room temperature butter into a mixing bowl. Add sugar.
Using the paddle attachment or a hand mixer, mix on medium-low until the butter is smooth, creamy, fluffier and light colored, about 2-3 minutes.
Add the egg yolk and vanilla, mixing until combined. Add the flour, salt, and baking powder. Mix on low just until large sticky clumps start to form. The batter will look dry and crumbly at first but as it gets mixed it will soften into a dough. Stop mixing just as the dough gets sticky, don’t overmix, otherwise the butter will soften too much and the dough will become very sticky.
Use a spatula to scrape the dough into a ball. Pick up the dough and shape it into a log/cylinder that is about 2” in diameter. Wrap the log in plastic wrap, twisting the ends of the plastic wrap to help keep a uniform cylinder shape. Place the log in the refrigerator.
Repeat the process for the chocolate cookie dough using the same mixing bowl.
Once both cookie logs have been made and wrapped tightly, allow them to chill in the refrigerator for at least 1 hour.
Once chilled, remove both logs from the refrigerator and cut each log lengthwise into quarters. If the dough seems brittle when cutting, it is too cold. Allow the dough to rest at room temperature for 15-20 minutes before cutting.
Pair one of the chocolate quarters with one of the vanilla quarters. Before sticking together, brush the cut side of one of the quarters with cold water to help the two pieces bond together. Repeat until you have 4 vanilla/chocolate matched log halves of cookie dough.
Pair 2 of the log halves together with the chocolate and vanilla sides alternating. Again, brush the cut sides of the halves with cold water to help them bond together.
After pairing those halves, you will have two cookie dough logs again. Gently press and roll each log to help the pieces bond together. Re-wrap each log in plastic wrap and place them back in the fridge.
Allow them to chill for 1 hour or for up to 2 days. You may also wrap foil over top of the plastic and place the logs into the freezer for baking later. You will need to bring the cookie dough closer to room temperature to be able to slice and bake when you are ready to make your cookies from frozen.
Preheat the oven to 350°F and line two baking sheets with parchment paper.
Remove the cookie dough logs from the refrigerator, unwrap, and slice ¼” thick cookies. If the cookie dough seems brittle when you start to cut it, allow it to rest at room temperature for 10-15 minutes.
Slice off as many cookies as you want, or slice both logs. Place the cookies on the baking sheets, leaving about 1” of space between each cookie.
Bake for 14-16 minutes. The cookies will seem soft when they come out of the oven, but they will firm up as they cool. Allow them to cool on the rack before transferring so they will not be as fragile.
Store cooled cookies in an airtight container at room temperature.