Mix broth, onion, tomato, chiles, and garlic. Bring to boil on high heat; cover.
Reduce heat to medium and simmer 10 minutes.
Take melted butter add to flour. Return this mixture back to heat on the stove and cook 3 minutes.
Stir in 3 1/2 cups of the hot milk; add 1/2 cup at a time. Cook 7 minutes until thickened.
Remove broth from heat and stir into milk mixture 1/4 cup at a time.
Return to heat; add remaining 1 1/2 cups of hot milk, salt, pepper, and cheese.
Stir until cheese is melted and soup is well heated.
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