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Preheat an outdoor grill to medium-high or an indoor grill pan over medium-high heat. Grill hot dogs or sausage until cooked through and browned on the outside.
In a medium saucepot over medium-high heat, melt butter. Once melted, whisk in flour and cook until fragrant, about 30 seconds. Rapidly whisk in beer, followed by the milk, and whisk until smooth. Bring to a bubble and thicken then remove from heat. Stir in cheese and mustard until combined and reserve.
Using a thin, serrated knife, cut into the rolls all the way from one side and scoop out some of the inside of the roll in a circle. (You can toast these inside pieces and process them into pretzel breadcrumbs for another recipe-YUM!) Pop the rolls in a low oven or toaster oven to soften.
To assemble dogs, carefully spoon some cheese sauce into the opening of the rolls, moving them around to make sure all the walls of the inside are evenly coated. Place hot dog into the opening and serve.