Preheat oven to 350 degrees F with the racks in the upper and lower thirds of the oven.
In a small bowl, whisk together flour, baking soda, and salt. In a stand mixer fitted with the paddle attachment, cream butter and sugars until light and fluffy. Slowly add egg and continue mixing. Slowly add flour mixture, oats, peaches, walnuts, and white chocolate chips. Mix until combined.
Line 2 sheet trays with parchment. With wet hands make 20 balls from the dough placing evenly among sheet trays. Press down on cookie dough with palm of your hand to make a flat circle.
Bake for 10 to 12 minutes or until golden and still a bit tender in the center. Remove from oven and let sit on sheet trays 1 minute. Remove to cooling racks to cool completely.