Bring potatoes, carrots, chile, red pepper flakes, turmeric, 1 cup water, and salt to a boil in a 3- to 4-quart heavy pot, then simmer briskly, uncovered, until vegetables are almost tender, about 5 minutes. Add zucchini and peas and simmer 1 minute more. Meanwhile, blend coconut, cumin, cayenne, and remaining 3/4 cup water in a blender or food processor to a medium-fine paste. Add coconut mixture to vegetable mixture along with yogurt. Simmer, uncovered, stirring occasionally, until vegetables are tender and flavors have blended, 12 to 15 minutes. If mixture becomes too thick to simmer, add more water. Serve sprinkled with curry leaves and drizzled with coconut oil, if desired.