Preheat oven to 400 degrees F . *Roasting Squash: Cut both acorn squash in half, scrap out and discard seeds and string. Rub 1 tablespoon of olive oil on inside and outside of all pieces of squash. Lay each piece face down onto a sheet pan and bake until tender, about 15 to 20 minutes. <p>Meanwhile, in a medium saucepan, heat remaining olive oil over medium heat and add mushrooms, onions, garlic and thyme, season with salt and pepper. Sauté until mushrooms are golden brown and onions are soft and tender, about 5 minutes.</p><p>Add rice and broth and bring to a boil. Lower heat, cover and simmer, until liquid is absorbed, about 15 to 20 minutes. </p><p>Remove squash from oven, carefully scoop out 3 tablespoons of flesh from each squash half and stir into rice. Season again with sea salt and pepper. Divide rice mixture evenly into squash halves, sprinkle with cheese and broil in oven 1 to 2 minutes. </p><p>Serve hot. </p>