Preheat oven to 425 degrees and line a rimmed baking sheet with parchment paper.
Cut acorn squash in half, lengthwise. Scoop out and discard seeds. Brush with 2 tablespoons olive oil and sprinkle with ½ teaspoon salt.
Place squash flesh side down on baking sheet parchment and bake until squash is easily pierced through with a fork, about 30 minutes. When done, remove pan from oven and leave the oven on.
While the squash bakes, heat 1 tablespoon oil in large skillet over medium high heat. Add sliced mushrooms, onions and cook until soft, 4-8 minutes. Add garlic and cook 1 minute. Stir in quinoa and cook 1-2 minutes to toast the quinoa somewhat.
Stir in broth, milk, remaining salt and black pepper. Add thyme sprigs and bring mixture to a simmer. Cover, reduce heat to low, and cook until quinoa absorbs all liquid and is fluffy, 15-20 minutes.
Remove lid and remove thyme sprigs if used. Stir in 3 tablespoons Parmesan cheese. When melted turn heat off.
When squash is baked and removed, turn each half over in the baking pan and fill each equally with the quinoa mixture. Sprinkle remaining cheese on each half and return to oven until tops are golden and squash is hot, up to 15 minutes.
Remove from oven and drizzle balsamic glaze over squash halves. Garnish with pomegranate seeds and serve right away.
Once baked the finished acorn halves can be wrapped and stored in the refrigerator up to 4 days. Remove wrap and warm in oven at 350 degrees about 15 minutes or until hot.