Spray a large nonstick soup pot or Dutch oven with nonstick cooking spray.
Add the onion and cook over medium heat, stirring often, until the onion begins to soften, about 5 minutes.
Add the broccoli, potatoes, carrot, broth and basil. Turn up the heat and bring to a boil then turn the heat to low and simmer, with the pot covered, until the vegetables are tender, about 20 minutes.
Transfer the mixture to a blender and puree until smooth. (Or use a stick blender to puree the vegetables right in the pot.)
Pour the puree back into the soup pot. Add the milk and stir occasionally until heated through.
Remove pan from the heat and let cool for about 1 minute.
Add the cheese and stir until it's melted. Adjust salt and freshly ground black pepper to taste.
Notes
Serving size: 1-1/2 cupsWW Points: 5Check the WW Points for this recipe and track it in the WW app. (Must be logged into WW on a smartphone or tablet.)8SmartPoints (Green plan)8SmartPoints (Blue plan)5SmartPoints (Purple plan)7PointsPlus (Old plan)I used 1 can of evaporated skim milk and 1-1/2 cups fresh skim milk. The evaporated milk adds some richness without extra fat.If the soup seems too thick, you can thin it with a little more milk. For a chunkier soup, just puree part of the soup.