Preheat oven to 350°F. Grease and flour a 12 cup bundt cake pan or 2 8" round cake pans.
Quinoa should be cooked a little soft so it is easy to blend into a smooth paste. Grind the cooked quinoa into a smooth paste using an immersion blender. Add milk as needed to get to a smooth consistency.
Combine milk, eggs and vanilla in a food processor. Pulse until well combined. Next add melted butter and quinoa paste and pulse until smooth and mixed through.
In a medium bowl, whisk sugar, cocoa powder, baking powder, baking soda and salt.
Add the contents of the food processor to the dry ingredients and gently mix until just incorporated. Do not over mix.
Pour the batter into the prepared baking pan and bake for 50-60 minutes if using the bundt cake pan and 40-45 minutes if using the smaller cake pans.
Let cool in the pan for 10 minutes before removing it onto the wire rack to cool completely.