Step 1

Preheat oven to 450 degrees. On a rimmed baking sheet, season cut sides of squash with salt and pepper, drizzle with 1 tablespoon oil, and turn cut sides down. Cover sheet tightly with foil and roast until tender, about 35 minutes.

Step 2

Meanwhile, in a medium straight-sided skillet, heat remaining 2 tablespoons oil over medium-high. Add mushrooms, onion, and thyme; season with salt and pepper. Saute until mushrooms are golden, 8 minutes. Add rice and broth and bring to a boil; cover and reduce heat to low. Cook until liquid is absorbed, 20 minutes.

Step 3

Remove squash from oven and heat broiler. Carefully scoop out 2 to 3 tablespoons flesh from each squash half and stir into rice; season with salt and pepper. Divide rice mixture among squash halves, sprinkle with Parmesan, and broil until melted, 2 minutes.