Melt butter in stock pot.
Add chopped onion and saute for five minutes until translucent
Add chopped zucchini and salt and saute for an additional five minutes until softened
Add chicken broth and peppers and bring to a boil. Turn down and let simmer for 20 minutes
Remove from heat and add chopped basil. Purée with an immersion blender, or, if you don't have an immersion blender (which you need to make your life complete), then purée in batches in a blender. At this point you can freeze the base and then reheat before adding in the half and half.
Add half and half and bring back up to a simmer
Taste for salt and pepper and adjust to taste. Serve hot