Creamed Eggs and Cheese

From 1912:

Cook together a tablespoonful each of butter and flour until they bubble, pour upon them a cup and a half of milk and stir until your sauce is smooth and thickened. Put in, then, a half cupful of grated dairy cheese and cook until this is melted and blended with the sauce. Have ready four hard boiled eggs, cut the whites from the yolks, and chop the whites fine. Add them to the sauce, season with a scant teaspoonful of salt and a dash of cayenne or paprika and turn upon buttered toast laid in a hot dish. Put the yolks through a vegetable press and strew over the tops of the whites and sauce.