In medium saucepan, heat oil over medium heat. Add rice and grated squash. Cook, stirring often, for 2 minutes. Add stock, water, and fish sauce or tamari and allow mixture to come to a boil. Reduce heat to medium-low, partially cover with lid, and let simmer, stirring occasionally, until congee is creamy, about 90 minutes. Stir in white pepper and maple syrup.