What happened was that your sauce broke. When protiens are heated in excess of about 170' F., they start to tighten up, or in the case of your cream and cheese, coagulate into lumps and grains. Andy said it right. Heat the cream, butter, and garlic slowly, over low heat. Do not let it boil. When its hot enough, remove from the heat and add the grated cheese. The cheese will serve to cool the sauce a bit, but still melt smoothly into the sauce. The sauce is then poured over the cooked noodles or chicken, or whatever you are putting your Alfredo Sauce over.
Any cheese sauce behaves the same way. If you want a cheddar flavored sauce, make a simple Bechemel from blond roux, a dash of nutmeg, heavy cream, and a touch of yellow mustard. Remove from heat and let cool slightly. Stir in shredded sharp cheddar cheese until smooth and creamy. This is a great starting sauce for a very creamy mac and cheese.
Sauces thick end with egg yolk or a mixture of egg white and egg yolk will also break if over heated, and for the same reason. In fact, that film that appears on boiled milk, that's the protiens coagulation and sitting on top of the liquid.
Low and slow, that's the secret.
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