In a large pot, bring the water to a boil with the squash and corn. Cover and simmer over moderately low heat until the squash is just tender, about 15 minutes. Add the kidney beans and cook until the beans are hot. Transfer 3 cups of the squash mixture to a blender along with some of the liquid and 1/2 cup of the basil; puree. Return the puree to the pot and keep warm.
Meanwhile, in a large skillet, heat 2 tablespoons of the oil. Add the onion and bell peppers and cook over moderate heat, stirring occasionally, until softened, 8 minutes. Add the cumin, oregano and 1 teaspoon of the paprika and cook, stirring, until fragrant, about 4 minutes. Stir the vegetables into the stew and season with salt and pepper.
In a small saucepan, heat the remaining 1/4 cup of oil. Add the remaining 1 teaspoon of paprika and cook over low heat until fragrant. Transfer to a small bowl.
Ladle the stew into bowls. Swirl in the paprika oil, sprinkle with the remaining 1/4 cup of chopped basil and serve.