1. Preheat oven to 375°.
2. Weigh or lightly spoon flours, potato starch, and cornstarch into dry measuring cups; level with a knife. Combine flours, potato starch, cornstarch and next 5 ingredients in a bowl; stir with a whisk.
3. Place granulated sugar, brown sugar, and butter in a large bowl; beat with a mixer at medium speed until well blended. Beat in vanilla and egg. Gradually add flour mixture, beating at low speed until blended. Fold in walnuts and chocolate minichips.
4. Drop dough by level tablespoonfuls 2 inches apart onto baking sheets lined with parchment paper. Bake at 375° for 10 minutes or until edges of cookies begin to brown. Cool 5 minutes on pans. Remove from pans; cool completely on wire racks.