Buttercup Squash Stuffed with Wild Rice, Shiitakes, and Caramelized Leeks

1. Preheat the oven to 350. In a saucepan over high heat, combine the wild rice and water,cover, and bring to a boil. Reduce heat to medium-low, add 1/4 teaspoon salt, and cook covered, for 30 minutes. Stir in brown rice, cover, and cook 30 minutes longer. Remove from heat and set aside. If any liquid remains, drain it off. Lightly oil a 9x13-inch baking pan and set aside.
2. Season the squash halves with salt and place them in the prepared pan, cut side down. Add 1/4-inch of water to the pan and cover tightly with foil. Bake until slightly softened, about 30 minutes.
3. Split the leeks lengthwise, wash thoroughly, and finely slice them. In a medium skillet over medium heat, heat 1 tablespoon oil. Add leeks, season with salt, and cook uncovered for 10 minutes, stirring occasionally. Sprinkle with the sugar, and continue to cook, stirring occasionally, until nicely browned and soft, about 15 minutes. Stir in a tablespoon or two of water if the leeks begin to stick. Remove from the heat and set aside. 
4. In a large skillet over medium heat, heat tremaining 1 tablespoon oil. Add onion and celery and cook until softened, about 7 minutes. Stir in mushrooms, thyme, sage, pepper, and salt to taste. Cook until mushrooms are softened, stirring occasionally, about 5 minutes. Transfer mixture to a large bowl. Add the reserved rice, leeks, and parsley, and season to taste with salt. Mix thoroughly to combine well.
5. Turn the squash cut side up, and fill with the stuffing. Cover and bake until the stuffing is hot and the squash is tender, about 30 minutes. Serve hot.