Melt butter in a saucepan over low heat.
Sprinkle in flour and whisk together until combined. Cook over low heat for 2 minutes.
Pour in milk and beer, whisking constantly, and cook for an additional minute. Add mustard, paprika, and cayenne and whisk. Add cheese and whisk slowly, cooking for a couple of minutes or until smooth, melted, and very hot. Remove from heat and whisk in egg yolk, Serve immediately (while hot) over toast. Sprinkle with chopped chives before serving.
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