How to Make It
In a large heavy casserole, combine the beans with the pumpkin, chicken stock and water and bring to a boil. Cover and cook over low heat until the beans are barely tender, about 15 minutes, depending on the size and type of bean.
Heat the oil in a medium skillet. Add the onion and carrot and cook over moderate heat, stirring frequently, until lightly browned, about 8 minutes. Season with salt and pepper. Add this mixture to the beans and simmer for 15 minutes longer.
Add 1 cup of the corn kernels to the beans. Puree the rest of the corn in a blender. If the puree is very dry, add a ladle of the bean cooking liquid. Stir the corn puree and basil into the beans and simmer for another 15 minutes, stirring frequently; the corn puree will thicken the stew. If it gets too thick, thin the stew with hot water; it should be slightly runny. Taste; adjust the seasonings.
Heat the oil in a small skillet. Add the garlic and cook over moderate heat until golden, about 2 minutes; discard the garlic. Remove the skillet from the heat and stir in the paprika. Drizzle the stew with the paprika oil and serve hot.