In a separate saucepan, melt the unsalted butter over medium-low heat. Sprinkle in the all-purpose flour and cook, whisking constantly, until foamy and no longer raw-smelling but not browned, 2–3 minutes.
While whisking, gradually ladle in the hot infused liquid, a little at a time, whisking smooth after each addition. Bring to a gentle simmer; cook, stirring often, until velvety and it coats the back of a spoon, 8–10 minutes.
Season with the fine sea salt, white pepper, and nutmeg. If desired, strain through a fine-mesh sieve for an ultra-smooth sauce. Use warm, or press plastic wrap directly on the surface to prevent a skin as it cools.