Bring water to a boil in a medium saucepan. Stir in quinoa. Reduce to a simmer, cover and cook until the grains are tender and reveal their spiraled germ, about 15 minutes. Transfer to a large bowl and let cool for about 10 minutes.
Add eggs, beans, cottage cheese, scallions, flour, baking powder, salt, and cheese to the quinoa and stir until well combined. Poor into 9x13 pan.
Bake until puffed and a little brown on top, about 20 minutes.