Make the beurre manié by kneading 1TBSP butter and 2 TBSP flour together in a small bowl, using your fingers or a fork. If the butter isn’t room temperature, you can cut it into a small dice and it will be soft enough to knead in just a few minutes.
Heat 1 TBSP butter in a sauce pan over medium heat. Add the onions when the butter has melted but before it foams. Stir until soft but not brown, 2-3 minutes. If using oil instead of butter, place a bit of diced onion in the pan while the oil heats. When it sizzles, it’s ready to add the rest of the onions and proceed as above.
Stir in garlic and cook for an additional 30 seconds
Optionally, at this point you could deglaze the pan with a splash of wine, making sure to evaporate most or all of the liquid before proceeding.
Add the 1 ½ C milk and bring to a simmer over medium-low heat.
Once it’s simmering, whisk in the beurre manié, taking care it dissolves completely.
Simmer for about ten minutes, continuing to whisk or stir frequently with a rubber spatula to assure that the sauce doesn’t clump or cling to the sides of the pan.
Remove from heat and stir in the nutmeg (if using), salt, pepper, and cheese. Do not apply heat at this point, as that would tend to separate the cheese. Don't overdo the nutmeg--you don't want your sauce to taste like eggnog!