This would make a perfect mid-week meal. Quick to prepare and nutritious. It would go well with a warm dinner roll and a fresh green salad.
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Melt the butter in a soup pot. Add the chopped onions and cook for a few minutes until tender.
Add the flour and stir well with a wooden spoon to incorporate into the fried onion. Cook for a couple minutes, stirring until there are no lumps.
Add the broth and the milk, stir in and bring to a boil. Reduce the heat and let simmer for 15 minutes. Stir as needed so it does not scorch.
Add the broccoli florets and cook for 10 minutes longer or until florets are tender but not mushy.
Stir in the salt, pepper and hot sauce.
Stir in the shredded cheddar cheese. Shut off the stove and let sit until the cheese is melted. Stir gently to combine.