Broccoli Cheese Soup

1/2 Onion chopped
1/4 C Butter
1/4 C Flour
2 C Chicken Broth
2 Bunches broccoli
2 Carrots
8 oz Cheddar Cheese
2 C Half and Half

Put 1 Tablespoon of butter in a pot and saute the onion in the butter. Cut carrots into small strips. I often just use a potato peeler. Chop the broccoli into small pieces. Make a roux using the remainder of melted butter and flour. Put in pot and cook for 5 minutes over medium heat.
Add half and half stirring constantly. Then add chicken broth and let simmer for 20 minutes. Add vegetables and cook for 20 minutes over low heat or until vegetables are cooked to your desire. Add cheese. Salt and pepper to taste. Eat with some bread!