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Simmer chicken broth and chopped onion for 15 minutes in a covered saucepan, until onions are soft. (Because I just used dehydrated onions, it didn’t have to heat so long)
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Heat the milk in the microwave for 1 to 2 minutes.
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In a large stockpot, melt the butter.
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Add the flour and pepper, whisk and cook together for a couple of minutes.
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Whisk in warmed milk. Continue to stir and cook until the soup starts to thicken.
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Next add the chicken broth and continue to stir until well blended.
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Add the cheeses and steamed broccoli.