Line two baking sheets with parchment paper, baking mats, or if you don't have either, grease the sheet with vegetable shortening. Two baking sheets are needed, because the cookies need to cool on the cookie sheet for an hour after baking. Each sheet should hold 12 cookies each, for a total of 24 cookies. Next thing to decide, is if you want to bake one sheet at a time or two. If you are only baking one sheet at a time, then make sure your oven rack is in the center. If you are baking both sheets at once, then adjust the oven racks so that your oven is split into thirds. Once the oven racks are situated, preheat the oven to 300F. Then, we need to make a flax egg. To do this, combine 1 tablespoon of ground flaxseed with 3 tablespoons of boiling water in a small dish. Set aside for 5 minutes to let it thicken. It's also a good idea to weigh out your flour. If you are using Bob's Red Mill gluten free 1-to-1 baking flour, it's 4.8 oz/cup. If you are using regular all-purpose flour (not gluten-free), it's 4.25 oz/cup.
In a large mixing bowl, add the butter of your choice, extra light olive oil, granulated sugar, light brown sugar, flax egg, unsweetened applesauce, vanilla extract, and freshly squeezed lemon juice. Using an electric mixer, beat on medium speed for 1 minute to cream everything together.
To the large mixing bowl, add the gluten-free flour, gluten-free rolled oats, baking soda, iodized salt, and ground cinnamon. Using an electric mixture, mix on low speed for 45 seconds, or just until everything is combined. You can also manually mix with a large spoon. Be careful not to over mix.
Fold in chocolate chips and chopped walnuts.
Portion out your dough into 3 tablespoon dollops. Place dollops on cookie sheet with space inbetween, then use your palm to flatten it to a disk and shape it.
Bake cookies for 20-23 minutes, or until the cookies are golden brown around the edges. If you are baking both sheets at once, switch them halfway through. Remove cookies from the oven, and allow them to cool on the baking sheet for an hour. Store cookies in an airtight container for up to 5 days, or store them in the freezer for up to 3 months.