In a medium saucepan, melt the unsalted butter over medium heat.
Add the minced garlic to the melted butter and cook for 1-2 minutes, stirring frequently, until fragrant. Be careful not to let the garlic brown.
Slowly pour the heavy cream into the saucepan, whisking constantly to combine with the butter and garlic.
Bring the cream mixture to a simmer over medium-low heat, stirring occasionally. Allow it to simmer gently for 5-7 minutes, or until slightly thickened.
Gradually add the grated Parmesan cheese to the sauce, stirring continuously until the cheese is melted and the sauce is smooth and creamy.
Season the Alfredo sauce with salt, pepper, and a pinch of nutmeg (if using), adjusting to taste.
Continue to cook the sauce for another 2-3 minutes, stirring occasionally, until it reaches your desired consistency. The sauce should coat the back of a spoon and have a velvety texture.
Remove the saucepan from the heat and let the Alfredo sauce cool slightly before serving.
If desired, garnish the Alfredo sauce with chopped fresh parsley for a pop of color and freshness.