Preheat oven to 375 degrees F (190 degrees C). Pour 1 cup of water into 9x13 baking dish.
Place the butternut squash into the prepared baking dish, cut side down. Bake in preheated oven until squash is easily pierced with a fork, about 45 minutes.
Meanwhile, place the rice and remaining 1 cup of water into a saucepan. Bring to a boil, uncovered, over medium-high heat. Reduce heat to low, cover, and simmer until water is absorbed and rice is fluffy, about 20 minutes. Remove from the heat and fluff with a fork.
Heat the olive oil in a large soup pot over medium-high heat. Stir in the onion, and cook until tender and transparent, about 5 minutes. Push the onion to the sides of the pan and add the sausage to the middle of the pan; cook until crumbly and evenly browned.
Stir in the cooked rice and corn.
Scoop out cooked squash and place in a blender or bowl of a food processor. Discard squash peels. Pour chicken broth into the blender or bowl of a food processor with the squash. Blend until smooth, about 1 minute.
Dump squash mixture into a stock pot, then add the sausage mixture. Add more chicken broth until you reach the consistency you prefer.
Season with pepper, and salt to taste. If desired, stir in the heavy cream. Simmer soup over medium heat until heated through, about 15 minutes, but do not boil.