This lost recipe is not from a specific bygone restaurant. It comes from the pages of a 1902 edition of The Brooklyn Eagle, which seemed (if the online archives are any measure) to have printed recipes for its readers from time to time. No source is ever mentioned for any of the recipes. Things like Lobster Newberg, "Real Spanish Buns," Hermits (a kind of cookie) and Candied Chestnuts. I'm reprinting this particular one because I have never heard of a Baked Bean Rarebit. It seems to be simply a Welsh Rarebit with baked beans added to the mix.
Baked Bean Rarebit
Press half a pint of cold baked beans through a sieve and mix with half a teaspoon of salt and quarter a teaspoon of paprica. Melt two tablespoonfuls of butter in a saucepan and when hot add the beans and when it is hot stir in gradually one-half cup of milk. When smooth add three heaping tablespoonfuls of soft cheese chopped fine, and a teaspoon of Worcestershire sauce. Stir until the cheese is melted, then pour over very think toasted slices of brown bread.
Previous Recipes of the Lost City