Preheat the oven to 350 degrees F and line a 9" x 5" loaf pan with parchment paper (or spray with cooking spray).
Start by preparing the flax "eggs." Stir together the ground flax seed and water together in a small bowl. Allow mixture to sit, stirring occasionally, until thickened and the consistency of beaten eggs, about 15 minutes.
Transfer the flax "egg" mixture to a stand mixer, along with the almond butter and coconut oil. Beat until well-combined and creamy. Add the remaining ingredients (except chopped candy canes) and continue beating until well-combined. The batter will be thick and slightly crumbly - this is normal.
Transfer the brownie batter to the prepared loaf pan and smooth into an even layer. Sprinkle with chopped candy canes (if desired) Bake on the center rack of the preheated oven for 25 to 35 minutes, until set up and brownies are cooked to desired doneness (for fudgier brownies, bake 25 minutes, and for cakier brownies, bake 30 to 35 minutes).
Remove from the oven and allow brownies to sit for 30 minutes before pulling on the parchment paper and releasing them from the loaf pan. Sprinkle with sea salt (if desired), cut into squares, and enjoy.