In fine-mesh strainer, place rice and rinse well under cold water until water runs clear, about 30 seconds. Transfer rice grains to food processor and pulse until finely chopped.

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.

Divide warm congee among 4 serving bowls before topping with kimchi, edamame, Thai basil, cilantro, and sesame seeds. Enjoy while warm.