Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan and line the bottom with parchment paper.
In a blender, combine the cooked quinoa, milk, eggs, and vanilla extract. Blend until smooth.
Add the melted butter and blend again until fully combined.
In a mixing bowl, whisk together the sugar, cocoa powder, baking powder, baking soda, and salt.
Pour the wet ingredients from the blender into the dry ingredients and mix until well combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.