In a saucepan, caramelize the chopped onion until golden brown.
Add chopped broccoli and potatoes and cook for 7-10 minutes until broccoli is cooked. Add salt and pepper to taste. Set aside.
In another saucepan, melt the butter. Add the flour and mix vigorously while adding bits of milk until a thick soup forms. You can also add herbs of choice for flavor.
Blend the cooked vegetables with your desired appliance and add the the creamy mixture.
Add the American cheese and mix until fully combined.
Serve with croutons. Enjoy!