Preheat the oven to 400 degrees.
To prepare the squash, using a sharp knife, slice the ends from the squash. Stand the squash on the large flat end and slice down through the middle lengthwise, creating two equal halves. Use a spoon to scoop out the seeds and any stringy pieces.
Place the squash halves, cut side up, on a lined baking sheet or in a baking dish.
Brush the top of the squash with the olive oil. Season the squash generously with salt and pepper and sprinkle the brown sugar over top.
Bake for 40 to 60 minutes, until you can easily pierce the flesh with a fork. Timing will depend on the size of your squash, so start checking at 40 minutes.
To prepare the mushrooms, heat the butter and oil together in a large skillet over medium heat. When the butter is bubbly, add the mushrooms and cook for 5 to 7 minutes, until browned and caramelized. Add the garlic and cook for 1 minute.
Add the sherry, thyme, 1/2 teaspoon salt, and 1/4 teaspoon black pepper and bring to a simmer.
Reduce the heat to medium-low and simmer for 10 minutes, until the liquid is almost all absorbed by the mushrooms. Season the mushrooms to taste with salt and pepper.
Spoon the mushroom mixture into the roasted butternut squash halves and serve.