This soup was inspired by a total fridge, freezer and pantry raid — as many good soups are — and my love of pozole: a Mexican soup with many iterations that typically combines chiles, meat and hominy. This vegetarian soup is bulked up with vegetables and beans in place of meat.
Heat the olive oil in a large wide pot or Dutch oven over medium-high heat. Add the red onion and cook, stirring, until softened, 3 to 5 minutes. Add the squash, 2 teaspoons cumin, 3/4 teaspoon salt and a few grinds of pepper. Cook, stirring, until the squash is well coated, 3 to 5 minutes.
Put the chipotle and adobo sauce in a blender with 1/2 cup corn and 2 cups water; blend until smooth. Transfer the chipotle puree to the pot, along with 4 cups water, the hominy and black beans. Cover, increase the heat to high and bring to a boil. Uncover, adjust the heat to maintain a fast simmer and cook until the squash is tender and the soup has thickened slightly, 20 to 25 minutes.
Meanwhile, thin the sour cream with 2 to 3 teaspoons water. Thinly slice the radishes for topping.
Remove the soup from the heat and add the remaining 3/4 cup corn, the arugula and remaining 1/4 teaspoon cumin. Stir just to heat the corn and wilt the arugula; season with salt and pepper. Divide among bowls; drizzle with the sour cream and top with the radishes.