Preheat your oven to 350°F (175°C). This ensures that your cookies bake evenly.
In a large mixing bowl, combine the softened unsalted butter, granulated sugar, and light brown sugar. Using an electric mixer or a whisk, cream these ingredients together until the mixture is light and fluffy.
Add the large egg and pure vanilla extract to the butter-sugar mixture. Beat until well combined, scraping down the sides of the bowl as needed.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. This step helps to evenly distribute the leavening agent and prevents any clumps.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to overmix, as this can lead to tough cookies.
Gently fold in the broken Kit Kat pieces and white chocolate chips, ensuring they are evenly distributed throughout the dough.
Using a spoon or cookie scoop, portion the dough onto the prepared baking sheet, leaving some space between each cookie, as they will spread while baking.
Place the baking sheet in the preheated oven and bake for 10-12 minutes, or until the edges are lightly golden but the centers are still soft.
Once baked, remove the cookies from the oven and let them cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.