Preheat the oven to 350°F. Line 1 to 2 rimmed baking sheets with parchment paper and set aside.
In a small bowl, whisk together the flaxmeal and water. Set aside to thicken. This is the flax "egg."
In the bowl of an electric mixer, cream together the cold vegan butter, brown sugar, and cane sugar until smooth. Add the vanilla and flax "egg" and mix until smooth.
In a separate mixing bowl, combine the oats, oat flour, baking soda, baking powder, cinnamon, and salt.
Slowly add the oat mixture to the butter and sugar mixture and beat until well combined. Stop the mixer and scrape down the sides and bottom of the bowl and beat again to ensure all the ingredients are properly incorporated.
Add the dried cranberries and chopped walnuts and stir to evenly distribute throughout the dough.
Roll the dough into balls 2 heaping tablespoons at a time and place onto the prepared baking sheet. Space out the cookie dough with at least 2 inches in between each one. These cookies will spread.
Bake for 10 to 12 minutes until the cookies have spread and the edges are starting to set.
Remove from the oven and let the cookies rest on the baking sheet for 3 to 4 minutes before removing to a wire cooling rack to cool completely.
Repeat with the remaining dough.