Heat the oil in a large saucepan with a tight-fitting lid over medium heat. Add onions; sauté for 5 minutes. Add potatoes and zucchini; sauté for 5 minutes; season with salt and pepper to taste.
Add broth and whisk up all of the browned bits from the bottom of the pan. Bring mixture to a boil then reduce heat, cover and simmer for 30 minutes.
Add mint and cook for 10 minutes. Transfer mixture to a blender (or use an immersion blender) and puree until smooth. Top each serving with cheese.