Place pretzel pieces in a food processor and pulse into pretzel crumbs the consistency of panko; place them in a shallow dish. Fill 2 more shallow dishes with flour and eggs and season everything with salt and pepper.
For the sauce, heat a saucepot over medium heat. Add butter and melt then whisk in flour. Add milk, let thicken slightly then whisk in beer and thicken. Season with granulated garlic and onion and cayenne. Remove pot from heat and stir in mustard and shredded cheese until melted and smooth.