Bring the quinoa and water to a boil in a medium saucepan. Cover, reduce to a simmer and cook for 10 minutes. Turn off the heat and leave the covered saucepan on the burner for another 10 minutes. Fluff with a fork and allow the quinoa to cool.
Preheat the oven to 350°F. Lightly grease two 8-inch round or square cake pans. Line the bottoms of the pans with parchment paper.
Combine the milk, eggs and vanilla in a blender or food processor. Add 2 cups cooked quinoa and the butter and continue to blend until smooth.
Whisk together the sugar, cocoa, baking powder, baking soda and salt in a medium bowl. Add the contents of the blender and mix well. Divide the batter evenly between the 2 pans and bake on the center oven rack for 40 to 45 minutes or until a knife inserted in the center comes out clean. Remove the cake from the oven and cool completely in the pan before serving. Frost if desired. Store in a sealed container in the refrigerator for up to 1 week or freeze for up to 1 month.