Note: This dough requires chilling.
Cream butter and brown sugar in a stand mixer bowl fitted with a paddle attachment. Mix in egg and vanilla until smooth. Add pudding mix, baking soda, and salt. Mix until combined. Mix in flour, then stir in sprinkles and M&Ms.
Scoop 2 tablespoon balls of cookie dough onto a cookie sheet covered with parchment or a silpat baking mat. Chill for at least 30 minutes.
Preheat oven to 350°F. Line cookie sheets with parchment paper. Place chilled cookie dough balls 2 inches apart on cookie sheet. Bake 9-11 minutes or until edges begin to turn brown. Cool for 5 minutes on cookie sheet before transferring to a rack.
Store in an airtight container for up to 4 days or freeze for up to one month.