In the bowl of a stand mixer, cream the butter and brown sugar on medium speed. Beat in the egg and vanilla extract until smooth.
Add the pudding mix, baking soda, and kosher salt. Mix until combined. Add the flour. Mix again until well combined. Scrape down the sides of the mixing bowl as needed. Add the sprinkles and M&Ms and mix on medium-high speed until they are well distributed throughout the cookie dough.
Line a baking sheet with parchment paper. Scoop ~1.5 tbs balls of dough onto the prepared cookie sheet. Cover and chill for at least 1 hour.
When you’re ready to bake the cookies, preheat the oven to 350 degrees F. Line two baking sheets with parchment paper. Place the chilled balls of cookie dough on the prepared baking sheets, approximately 2 inches apart. Bake 9-11 minutes, or until the edges just start to turn brown.
Remove the cookies from the oven and press additional white chocolate chips into the warm cookies, if desired. Allow the cookies to cool on the baking sheets for 5 minutes before removing them to a wire rack to finish cooling completely.