Preheat the oven to 350°F. Lightly grease an 8x8 baking dish or line it with parchment paper.
Prepare the flax eggs. Stir together the ground flax and water in a small bowl. Set aside for at least 10 minutes.
In a large bowl or stand-up mixer, combine the brown rice flour, carob powder, coconut sugar, almond flour, buckwheat flour, tapioca flour, baking powder, and sea salt. Stir until blended.
In a separate large mixing bowl, combine the flax eggs, coconut milk or almond milk, pumpkin puree, tahini, coconut nectar or maple syrup, and vanilla extract. Whisk until creamy.
Pour the wet mixture into the bowl with the dry ingredients and beat until a batter is formed. Add the chopped walnuts if using and beat again or use a spatula to fold the pieces into the batter. Transfer the batter to the baking dish. Bake for 27 to 30 minutes until edges have started to crust and pull away from the edges of the baking pan (middle will still “jiggle” and appear darker and undercooked, but it will set as it cools). Allow the brownies to cool in the baking dish (at least 1 hour).