Melt butter in a small saucepan set over medium heat. In a medium-size bowl, stir flour with sugar. Then whisk into melted butter until mixture is moistened. Stir in milk until smooth. Cook, whisking frequently, until thickened and smooth, about 5 minutes. Stir in brandy and vanilla. Remove from heat.
Serve right away over Apple Coffee Cake with Brown Sugar Sauce. Or cover and refrigerate for a week or more. Reheat just before serving.