Preheat oven to 350 degrees F (175 degrees C). Grease a rectangular cake pan.
Blend quinoa, butter, eggs, milk, and vanilla extract together in a blender until smooth.
Combine sugar, cocoa powder, baking powder, baking soda, and salt together in a large bowl. Stir quinoa mixture into sugar mixture until batter is well combined. Fold chocolate chips and pecans into batter; pour into the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, 40 to 45 minutes. Cool cake on a wire rack.