Preheat the oven to 375ºF. Line a baking sheet with parchment paper, a silpat, or spray with cooking spray.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, shortening and sugars until they are light and fluffy. Add the vanilla and eggs and beat until it is light.
In a large bowl, combine the flours, oatmeal, salt, baking powder, and baking soda. Add about 1 cup to the butter mixture and blend. Mix in the milk, then the remaining dry ingredients. Fold in the nuts.
Drop the doughy by the teaspoon or with a small cookie scoop onto the prepared baking sheet. Bake 10-12 minutes or until the edges and tops are beginning to brown.