Preheat oven to 350ºF. Line a baking tray with parchment paper. Using an electric mixer (stand or hand), cream together butter and brown sugar. Beat until fluffy. Add vanilla and egg replacer or flax eggs. Scrape down bowl and beat just until everything is combined.
In a separate bowl, whisk together flours, cinnamon, salt, and baking soda. Add it to the butter mixture, mixing it until just combined. Add in oats and mix again.
Using a 2 tablespoon portion scoop or a regular tablespoon, drop dough onto prepared baking tray two inches apart. Bake for 13 to 15 minutes. Bake longer for a crisper cookie. Remove tray from oven and let cookies cool slightly before transferring to a wire cooling rack or plate. If you try to remove the cookies too soon, they may break. Serve warm or chill and fill with a scoop of vegan ice cream for a real treat!