Preheat the oven to 375 degrees F. Line three baking pans with parchment paper and set aside.
Whisk the flours, baking powder, salt and xanthan gum together in a medium bowl.
Put the sugar, applesauce, coconut oil, grapeseed oil, vanilla and vinegar in a large bowl and beat with an electric mixer on low speed until combined, about 1 minute. Add the flour mixture to the bowl with the wet ingredients, alternating with 1/3 cup water, until fully combined. Fold in the chopped walnuts.
Spoon heaping tablespoons (or a small scoop) of the dough onto the baking sheets, 1 inch to 1 1/2 inches apart. Bake the cookies in two batches, two sheets at a time, until the cookies are set and slightly browned around the edges, 18 to 20 minutes.
Remove from the oven and let the cookies cool on the sheets for 2 minutes, and then remove to a rack and cool completely. Bake the remaining cookies on the third pan following the above directions.
Vegan Cinnamon and Pecan Cookies: Make the Vegan Vanilla Cookies with Walnuts, adding 1 1/2 teaspoons ground cinnamon to the flour mixture, and folding in 1 cup chopped pecans instead of the walnuts. Bake as directed. Vegan Chocolate Peanut Butter Cookies: Make the Vegan Vanilla Cookies with Walnuts, adding 1/3 cup natural peanut butter to the wet ingredients, and increasing the water to 2/3 cup. Substitute in 3/4 cup chopped roasted unsalted peanuts in place of the walnuts in the recipe. Vegan Rocky Road Chocolate Whoopie Pie Cookies: Make the Vegan Vanilla Cookies with Walnuts. Add 3/4 cup vegan chocolate chips and replace walnuts with 3/4 cup chopped raw almonds. When cool place 3 mini vegan marshmallows on each of 18 overturned cookies, and broil 1 minute. Top each with another cookie to make sandwiches.
From Food Network Kitchens