For the sauce: In a small saucepan, heat 1 cup evaporated milk over medium heat until hot but not yet boiling. In a small bowl, toss together the cheese, cornstarch, and ground mustard. Turn the heat on the evaporated milk down to a very low heat, then whisk in cheese until melted. Mixture will thicken as it warms. Keep warm, and thin with a little more evaporated milk if the mixture gets too thick.
For the meat: Heat a tablespoon or so of olive oil in a large cast iron skillet or other skillet. Season beef with salt and pepper. When oil is hot, add meat and sear evenly until browned. This should only take a few minutes. Once beef is just browned, add caramelized onions, Worchestershire sauce, and sugar. Stir to combine and cook until liquid is evaporated and onions are warm, about another minute.
Split rolls down the middle and spread the inside cut edges with butter. Place under broiler and toast until golden brown, about 1-2 minutes. Scoop beef into toasted rolls, then top with white cheddar sauce. Serve.
Notes
For the freezer: uncooked sliced meat, caramelized onions, and grated white cheddar can be frozen separately in small freezer bags to cut out the prep time.