Melt the butter: In a medium saucepan, melt the butter over medium heat until it foams but does not brown, about 1 minute.
Make the roux: Whisk in the flour and cook for 1 to 2 minutes, stirring constantly, until the mixture turns pale gold and smells toasted, not raw.
Add garlic: Stir in the minced garlic and cook for 30 seconds, just until fragrant, being careful not to let it brown.
Pour in the milk: Add the milk in a slow, steady stream while whisking constantly, so no lumps form in the roux.
Add the broth: Whisk in the broth, then increase the heat slightly to bring the sauce to a gentle simmer.
Simmer until thickened: Cook, stirring often, for about 5 minutes, until the sauce coats the back of a spoon and leaves a clear trail when you run a finger through it.
Melt in the cheese: Reduce the heat to low and stir in the Parmesan cheese until it melts fully and the sauce looks glossy.
Season the sauce: Stir in the nutmeg, then season with salt and black pepper to taste, adjusting until the flavor feels balanced.
Adjust the consistency: If the sauce is thicker than you'd like, whisk in a little more warm milk or broth, a tablespoon at a time.
Use or store: Use the sauce right away over pasta, chicken, or vegetables, or let it cool and store it in an airtight container in the fridge.
