Preheat the oven to 350ºF and line or grease a loaf pan.
In a small bowl, combine the ground flax and water to create a flax egg and set aside.
In another small bowl, combine peanut butter and maple syrup to create the peanut butter swirl mixture and set aside.
In a medium-sized bowl, mix together the peanut butter and coconut sugar until fully combined.
Once the flax egg has gelled up, stir it into the peanut butter and coconut sugar mixture followed by the remaining wet ingredients.
Sift the dry ingredients onto the wet and stir until combined.
Pour the batter into the loaf pan then dollop the peanut butter swirl mixture on and swirl into the brownie batter using a chopstick or toothpick.
Bake for 15-20 minutes then allow to set and cool completely in the pan.