Start by melting the butter in a medium saucepan over medium-low to medium heat. Make sure it doesn't brown; you want it just melted for the sauce base.
Next, add the heavy cream to the melted butter and bring it to a gentle simmer. Cook and whisk the cream often for about 5 minutes until it starts to thicken slightly.
Once the cream is simmering, add the minced garlic to the saucepan. Cook for another minute, allowing the garlic to soften and release its flavor.
Slowly add the freshly grated Parmesan cheese a little at a time while whisking constantly. Continue to stir until all the cheese is melted and the sauce is smooth and creamy.
Finally, season the Alfredo sauce with salt, freshly cracked pepper, and a pinch of freshly grated nutmeg if desired. If the sauce becomes too thick, you can thin it out with a bit of extra cream or some pasta water.
Notes
Use fresh Parmesan cheese, save pasta water for added moisture, adjust consistency with cream or pasta water, control the heat to prevent burning, and experiment with flavors by adding herbs or vegetables.