Heat the oven to 375°F and grease a 3-quart baking dish.
Simmer the quinoa in the vegetable broth, covered, for 15 minutes, then remove it from the heat and let it stand for 5 minutes.
Steam the broccoli for 3 minutes, until bright green but still firm, and drain it thoroughly.
Melt the butter in a saucepan, whisk in the flour and garlic powder for 1 minute, then gradually whisk in the milk.
Simmer until the sauce coats a spoon, remove it from the heat and stir in the mustard, 2 cups cheddar, salt and pepper.
Fold the quinoa, broccoli and cheese sauce together in the baking dish and top with the remaining cheddar.
Bake for 20 to 25 minutes, until bubbling and browned along the rim.
Rest for 5 minutes before serving.