Preheat the oven to 350°F.
Brush the inside of the squash halves with the oil and maple syrup. Sprinkle with the cinnamon. Place the squash cut side down in a baking dish and bake for 35 minutes, or until tender. While the squash bakes, prepare the filling.
Warm the olive oil in a medium heat. Add the onion and sauté for 8 to 10 minutes, or until soft, stirring occasionally. Add the garlic and cook for 1 minute longer. Add the mushrooms, sage, and thyme. Continue sautéing for 2 to 3 minutes, until the mushrooms are tender and release their juices. Add the water or vegetable broth, and soy sauce. Simmer for 1 minute, to blend the flavors. Stir the cornstarch mixture, and add it to the skillet. Reduce the heat to medium-low and cook for 2 to 3 minutes, until the sauce thickens. Stir in the rice. Salt and pepper to taste.
Place each squash half in a shallow serving bowl. Spoon the rice mixture into the baked squash, top with chopped parsley, and serve immediately.