Heat the oil in a large pot over medium-high heat. Add the onion and jalapeño and cook until softened and the onion is translucent, about 5 minutes.
Add the apple and butternut squash and cook until slightly softened, about 5 minutes. Add the corn, salt, curry, cumin, garam masala, and pepper and cook until fragrant, about 2 minutes.
Add the vegetable broth and bring to a boil. Reduce the heat and simmer, partially covered, until the squash is tender, 25 to 30 minutes.
Puree the soup with a blender. Stir in the coconut milk
Serve the soup swirled with more coconut milk and sprinkled with mint.