01 - Preheat the oven to 375°F. Lightly grease a 9x13-inch baking dish with olive oil or butter.
02 - Prepare the quinoa according to the package directions. Fluff with a fork and set aside.
03 - Heat olive oil in a large skillet over medium heat. Cook the onion until softened, about 3 to 4 minutes. Add the garlic and cook for 1 minute. Stir in the broccoli and sauté until just tender, about 5 minutes for fresh or until heated through for frozen.
04 - In a large bowl, whisk together the eggs, milk, sour cream or yogurt, thyme, paprika, salt, and pepper. Fold in the cooked quinoa, sautéed vegetables, and 3/4 cup of the shredded cheese until evenly distributed.
05 - Transfer the mixture into the prepared baking dish and spread it into an even layer. Scatter the remaining cheese and breadcrumbs over the top.
06 - Bake uncovered for 30 to 35 minutes, until the top is bubbly and golden brown. Let the casserole rest for 5 minutes before slicing and serving.