8ozgrated sharp cheddarwhite or yellow cheese (about 2 cups)
Instructions
In a medium saucepan over medium heat, saute onion in 1 tablespoon of butter until caramelized (browned), remove from pot and reserve. About 5-7 minutes.
Place remaining ¼ cup of butter in the same saucepan, melt completely, whisk in flour, whisking constantly over medium heat until thickened and golden brown, about 2-3 minutes. Slowly, while whisking pour in half-and-half, will thicken up very quickly, keep adding until combined.
Add chicken broth (start with 4 cups) and whisk well to combine, bring to simmer (it'll take 3-5 minutes, watch closely, it will rise up quickly). Add broccoli, carrots and reserved caramelized onions, cover, simmering about 15-20 minutes until tender. If too thick, add more broth, up to 2 cups.
Add salt and pepper to taste. Remove 1-2 cups of the chunky mixture and blend in blender or lightly blend directly in the pot using an immersion blender. Return to soup pot and stir to combine. This will yield a smoother, creamier soup, but it's not necessary. Return to low heat and adding shredded cheese, stirring until completely melted.