Onion Béchamel

Melt butter in large saucepan over low. Add flour, and slowly whisk until it resembles wet sand. Cook over low, whisking constantly, until mixture is shiny and smells toasty, about 2 minutes. Whisking constantly, gradually add cold milk. Once fully combined, switch to a wooden spoon. Add onion half, salt, and nutmeg. Cook over low to medium-low at a very gentle simmer, stirring very often, until onion is cooked through and sauce is very thick, about 45 minutes. Pour through a fine wire-mesh strainer; discard solids. Use warm, or refrigerate as directed.