In a medium-sized saucepan, melt the butter over medium heat. Be careful not to let it brown.
Once the butter is melted, add the minced garlic. Sauté for about 1-2 minutes until fragrant, but not browned.
Pour in the heavy cream and bring the mixture to a simmer. Stir continuously to prevent scorching.
Gradually add the freshly grated Parmesan cheese to the saucepan, stirring constantly until the cheese melts and the sauce becomes smooth.
Add salt and black pepper to taste. Remember, Parmesan cheese is already salty, so taste as you go to avoid over-salting.
Let the sauce simmer for a few more minutes until it thickens to your desired consistency. If the sauce becomes too thick, you can thin it out with a bit more cream or a splash of milk.
Remove from heat and pour over your favourite pasta. Garnish with chopped fresh parsley if desired.