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