Heat the olive oil in a Dutch oven over medium-high heat. Cook and stir the garlic and onion in the oil until soft and translucent. Add the butternut squash and corn and cook for 3 more minutes. Pour the stock into the Dutch oven and bring to a boil; season with basil and black pepper.
Reduce the heat to medium-low and simmer uncovered until the squash is tender, about 15 minutes. Remove the Dutch oven from the heat and using a hand blender, or working in batches with a counter top blender, process the soup until smooth. Stir in the yogurt and nutmeg.
