Preheat oven to 350 degrees F. Line a baking sheet with parchment paper or a Silpat baking mat and set aside.
Using a mixer, beat together butter and sugars until creamy. Add in white chocolate pudding mix, eggs, and vanilla extract. In a medium bowl, whisk together the flour, baking soda, and salt. Add the dry ingredients to the wet ingredients and mix until just combined. Stir in the Oreos and white chocolate chips.
Drop cookie dough by rounded tablespoons onto prepared baking sheet. Bake for 10 minutes, or until slightly golden around the edges and set. Remove cookies from oven and let cool on baking sheet for two minutes. Transfer to a cooling rack and cool completely.
Note-these cookies will stay soft for 3-4 days. Store in an air-tight container on the counter.
