Heat the oil in a saucepan over medium heat. Add the kabocha, curry powder, ginger, and turmeric to the pot and stir-around, letting the cubes of squash lightly brown. Add the shrimp paste and cook for a minute longer.
Add the beans and cook for another 2 minutes, until the beans are lightly browned.
Add the coconut milk, water, sugar, and salt (about 1/2 teaspoon) to the pot and let the liquid simmer for 20 minutes, until the beans and squash are tender but not mushy. Serve warm.