Preheat oven to 325ºF. If using flax eggs, combine ground flaxseed and 5 Tbsp. water in a small bowl. Set aside. Skip step if using eggs.
In the bowl of a food processor, combine almond flour, tapioca starch, cocoa powder, baking powder, pinch of salt, and coconut sugar. Pulse a couple times until well mixed. Add in 2 eggs (for paleo/gluten-free) or flax egg (flax-water mixture; for vegan), melted coconut oil, maple syrup, almond butter, peppermint extract, and vanilla extract. Process until smooth. Alternately, to mix by hand, combine dry ingredients in a medium bowl and whisk well, then add in egg or flax egg, melted coconut oil, maple syrup, almond butter, and extracts, and stir until very smooth.
Line an 8x8” baking pan with parchment paper and spray with coconut oil. Scrape brownie batter into prepared pan, push batter into edges, and smooth surface. Bake 25-30 minutes or until a toothpick inserted into the center comes out close to clean. Don’t overbake! You don’t want the toothpick to be perfectly clean, but it should not be coated in what looks like frosting. When finished baking, remove from oven and let cool on a wire rack.
Make frosting: combine chocolate chips, coconut oil, maple syrup, and coconut cream in a medium microwavable bowl. Microwave 60 seconds then stir well. Continue microwaving in 30-second bursts, stirring very well between each burst, until chocolate is just melted. Stir in peppermint and vanilla extracts, then pour over still-warm brownies. Let cool slightly then top with crushed peppermint candies. Let cool completely before cutting. If frosting is not solidifying, chill for about an hour to harden.