Lightly coat a casserole dish (I used an 8x8 square dish) with non-stick spray or lightly grease.
Prepare quinoa using water or broth, according to package directions. You should end up with about 3 cups of cooked, fluffy quinoa. Place in a large mixing bowl.
While quinoa is cooking, steam broccoli for 5-6 minute or until bright green and crisp tender.
Meanwhile, shred cheese by using a food processor with the shredding attachment or with a handheld grater.
Preheat oven to 350°F.
Heat butter in a medium saucepan over medium heat. Add onion and garlic and cook until soft and fragrant, about 7 minutes. Meanwhile in a small bowl or measuring cup, whisk together milk, flour, garlic powder, salt and pepper. Pour milk mixture into saucepan with the onions and garlic. Allow sauce to simmer, whisking continuously until sauce has thickened, about 5 minutes. Remove from heat and whisk in 2 cups shredded cheddar cheese until melted.
Pour cheese sauce over quinoa and broccoli. Toss well to combine.
Transfer to greased baking dish and top with remaining shredded cheese.
Bake uncovered for 15 minutes or until the casserole is heated through and cheese has melted. Serve warm.