Preheat oven to 350°F. Grease several large baking sheets.
In large bowl, mix oats, both flours, baking soda and salt.
In small bowl, mix nut butter and oil until well blended. Stir in sugar, soy milk and vanilla until combined.
Add milk mixture to flour mixture and stir with a wooden spoon just until combined. Gently fold in chocolate chips and walnuts. For tender cookies, don’t overmix the dough.
Drop dough by large spoonfuls onto prepared baking sheets, spacing 2 inches apart. Bake until set and tops begin to look dry, 13 to 15 minutes. Let cool on baking sheets 5 minutes before removing to wire racks to cool completely.