Preheat the oven to 350°F (180°C). Line an 8-inch (20 cm) square baking dish with parchment paper.
Chop the chocolate into ½-inch (1 ¼ cm) pieces. Set aside half and melt the other half in a microwave-safe bowl for 45 seconds.
Make the flax egg: combine the ground flaxseeds with the water in a small bowl and mix with a fork. Set aside for at least 10 minutes to gel.
In a medium bowl, add the sugar and vegan butter and whisk until smooth. Then add the vanilla, flax eggs, and melted chocolate and whisk until well-combined.
Sift in the flour, cocoa powder, baking powder, and salt and fold with a spatula until all ingredients are combined. Be careful not to overmix. Then, stir in the reserved chocolate pieces.
Pour the batter into the baking dish and smooth the top with a spatula.
Bake for 30-35 minutes, until a fork inserted in the center comes out clean. Let cool for at least 20 minutes.