Let your milk come to room temperature or close to it in a measuring cup for about 20 minutes or so before starting, you can leave your butter out too so it melts faster.
Whisk flour and butter in a pan over moderate high heat, it’ll look like crumbles of pie crust when ready, about 5 minutes.
Add your milk in small pours, not all at once to prevent clumping, just a bit at a time while stirring. Continue stirring as sauce thickens another 7-10 minutes or so, or more if needed depending on heat, pan, milk used, etc.
When sauce coats the back of a spoon or a silicone whisk, season with salt, pepper, nutmeg, minced garlic and the grated Parmigiano-Reggiano cheese. Stir to combine and until cheese melts and sauce thickens more, 2-3 minutes.
Remove from heat and set aside, move to a measuring cup if you want to keep out of hot pan.