Gradually whisk in the milk and cream. Bring to a boil over medium heat, whisking constantly and scraping the sides and bottom of the pan. Simmer over low heat,
1 to 2 minutes. Remove from heat and add the gelatin, stirring until dissolved. Add the butter, stirring until melted. Stir in the rum and vanilla. To prevent a skin from forming, lay a sheet of plastic wrap directly on the surface of the hot cream. Let cool.