Preheat oven to 350 degrees F. Line a baking sheet with parchment paper or a silicone mat.
In a large mixing bowl, cream together butter, sugars, and pudding mix until creamy. Beat in eggs and vanilla until smooth.
Mix together flour and baking soda in a separate bowl. Then add to wet ingredients and mix until incorporated. Stir in white chocolate chips and cherries using a wooden spoon or spatula.
Drop cookies by tablespoonfuls onto prepared cookie sheets. Bake for 10-12 minutes or until edges are golden and cookies are set.
Let cookies cool on baking sheets for a couple of minutes before removing to a cooling rack to cool completely.