Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish.
In a large skillet over medium heat, add a splash of olive oil and sauté the chopped onion until translucent, about 5 minutes. Add the minced garlic and cook for an additional minute.
Stir in the diced butternut squash, cumin, thyme, salt, and pepper. Cook for about 5-7 minutes, until the squash begins to soften.
In a large bowl, combine the rinsed quinoa, vegetable broth, and the sautéed squash mixture. Mix well.
Pour the quinoa mixture into the prepared baking dish. Cover with foil and bake for 30 minutes.
Remove the foil, stir in the milk and half of the shredded cheddar cheese. Sprinkle the remaining cheese on top.
Return to the oven and bake uncovered for an additional 15-20 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let it cool for 5 minutes. Garnish with chopped parsley if desired before serving.