In a large soup pot or Dutch oven, heat oil over medium heat until hot.
Add onion, garlic, curry powder, salt and pepper and cook, stirring frequently, until onion and garlic are soft and starting to caramelize.
Add tomatoes, squash, kale and vegetable broth and cook, covered, until squash is tender, about 15 to 20 minutes.
Taste soup. Add additional salt and pepper, if desired.