Preheat your oven to 350°F (175°C). Lightly grease an 8x8-inch square baking pan or line it with parchment paper for easy cleanup.
In a small bowl, combine 1 tablespoon of ground flaxseed with 3 tablespoons of water and stir to mix. Let the mixture rest for approximately 5 minutes, allowing it to thicken and develop a gel-like texture.
In a spacious mixing bowl, combine the flour, baking powder, and salt, whisking until well blended.
In a different bowl, whisk together the melted coconut oil (or vegan butter), maple syrup, lemon juice, lemon zest, and vanilla extract until everything is fully blended.
Pour the wet ingredients into the dry mixture and stir until everything is just incorporated. Add in the flax egg and stir until fully incorporated.
Transfer the batter into the prepared pan, smoothing it into an even layer across the bottom.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean and the top is lightly golden.
Let the brownies sit in the pan for about 10 minutes to cool slightly, then gently move them to a wire rack to cool completely.
Once cooled, cut into squares. Optionally, dust with powdered sugar or drizzle with vegan lemon glaze for extra flavor!