Preheat oven to 350 F. Line baking sheets with parchment paper.
Blend the oats in a food processor to a fine powder. In a bowl, whisk together the blended oats with the flour, baking powder, baking soda and salt; set aside.
In a separate bowl, cream together the butter and both sugars until light and fluffy, 3-4 minutes. Scrape down the sides of the bowl and beat in the eggs one at a time, beating well after each addition. Beat in the vanilla extract.
Gradually add the flour mixture, mixing just until incorporated. Fold in the chocolate chips and walnuts.
Roll the dough into balls and place on the baking sheets. Bake until the edges are set but the center still looks undone, about 10 minutes.
