In a medium bowl, whisk together flour, cocoa, baking soda, and salt. Set aside.
In a large bowl with a handheld mixer or the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium-high speed until light and fluffy (approximately 2-3 minutes). Turn the mixer speed down to medium, add the egg and vanilla, and beat again until combined.
With the mixer on low, slowly add flour mixture and beat until just combined. Add the white chocolate chunks and cherries and continue mixing until evenly dispersed. Cover dough and refrigerate for at least 2 hours and up to 3 days.
When you are ready to bake the cookies, line a large baking sheet with parchment paper or a silicone baking mat. Set aside. Preheat oven to 350ºF.
Using a cookie scoop, roll the dough into balls and place on prepared baking sheet. Bake for 9-11 minutes, or until edges are set and center is no longer shiny. Remove from oven and allow to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely. Cookies stay fresh covered at room temperature up to 1 week. Baked cookies can be frozen, up to 2 months. Rolled cookie dough can be frozen, up to 3 months. Place on baking sheet and add 1-2 minutes to baking time.