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Boil the fettuccine according to package instructions. As the water preheats, begin the sauce.
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Melt the butter in a large saucepan over medium heat. Add the garlic and cook for one minute.
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Whisk in the flour. Gradually add the heavy cream, then the milk, whisking constantly.
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Reduce the heat to low once the sauce begins to bubble. It will continue to thicken as it simmers.
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Slowly sprinkle in the cheeses, continuing to whisk.
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Drain the pasta and carefully mix it into the sauce until well incorporated. The pasta will absorb the sauce an it will get thicker still.
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Garnish with chopped parsley, and serve!