Broccoli Cheddar Soup

1 TBLS melted butter
1 cup chopped onion
¼ cup melted butter
¼ cup flour
2 cups milk
1 cup ½ & ½ (or substitute and additional cup of milk)
4 cups chicken stock
1 lb or more of broccoli-chopped into small bits
1 cup carrots-chopped small
2 cups grated cheddar cheese

1. In a medium sauce pan melt ¼ cup butter. Add the flour and whisk together for about 3 minutes (stir continuously).
2. Add the milk, ½ and ½, and chicken stock. Simmer for 15 minutes, stirring occasionally.
3. Add the broccoli and carrots and simmer for another 20 minutes, or until the broccoli and carrots are soft.
4. Remove from heat and stir in grated cheddar cheese until melted.