Sort of a hot tuna and egg salad melt.
Here’s a not-quite-identical version from the April 16, 1961 edition of The Hammond (Indiana) Times:
To simplify the job of satisfying these hearty young appetites, try making sandwiches baked in foil, such as those prepared by the “Cook of the Week,” Mrs. Alden T. Schmidt of Highland. Not only are they easy for mother to fix, but they give a change from the traditional hot dog or hamburger, which will make a big hit with boys and girls alike.
One nourishing sandwich made by Mrs. Schmidt combines cheese, tuna fish and hard boiled eggs with accents of green pepper, olives, onion and sweet pickle. Appropriately named Bumsteads, the filling is spread on hot dog or hamburger buns, wrapped in foil and heated in the oven for 25 minutes.
1 cup (1/4 pound) sharp American cheese, diced
Combine all ingredients but the buns. Spread on bottom half of each bun. Wrap each bun in foil or waxed paper and place on baking sheet. Heat sandwiches at 325 degrees for 25 minutes. Sandwiches may be prepared well in advance of serving and stored in the refrigerator until needed.
This seems to be a Midwestern artifact of the 1950s and 1960s, inspired by the diversity of ingredients in sandwiches like the ones that that Dagwood Bumstead would eat in the Blondie comic strip, like this one from the December 8, 1955 edition of the Wichita Daily Times of Wichita Falls, Texas:
It’s a cousin to the more famous Dagwood sandwich, a pile of cold cuts and cheeses larger than one could eat, inspired by the volume of the comic strip’s lunchtime fare.
From a box sold in East Moline, Illinois.
1/4 lb. American cheese (cubed)
3 hard-cooked eggs
1 (7 oz.) can flaked tuna
2 Tbsp. chopped green peppers
2 Tbsp. chopped onion
2 Tbsp. chopped stuffed olives
2 Tbsp. chopped sweet pickle
1/2 cup mayonnaise
6 weiner buns
Combine ingredients. Mix thoroughly. Split buns and fill. Wrap in foil.
Place in oven, 250 deg. for 30 minutes or until thoroughly heated and cheese is melted.