Position racks in the upper and lower thirds of the oven and preheat to 350 degrees.
In a small bowl, whisk the flour, baking soda and salt. In a stand mixer fitted with the paddle attachment, cream the butter and light brown sugar, dark brown sugar and granulated sugar on medium speed until light and fluffy. Add egg and mix on low speed until incorporated. Slowly add the flour mixture, oats, dried peaches, walnuts, and white chocolate chips and mix until combined.
Line 2 baking sheets with parchment paper. With wet hands, make 20 balls from the dough and put on the prepared baking sheets, about 2 inches apart. Press down on the dough balls with palm of your hand to make flat circles.
Bake the cookies until golden and still a bit tender in the center, 15 to 17 minutes. Remove from oven and let sit on the baking sheets for 1 minute, then transfer the cookies to a rack to cool completely.