Melt the butter in a saucepan. Add the onion and garlic and sauté briefly over medium-low heat. (You need just a small clove, about ½ teaspoon minced.)
Next, quickly stir in the flour to make a paste. Add the chicken broth, whisking vigorously to avoid any lumps.
Continue whisking and quickly add the milk. Bring almost to a boil, stirring constantly.
Add the cheese and use a spoon to continue stirring until the cheese melts completely and blends into the soup.
Reduce heat to low and stir in the cream. Let the soup come back up to serving temperature, however do not let it boil! Salt and pepper to taste.
Serve hot with plenty of fresh bread—Cuban if you can find some!