How to Make It
Combine the mayonnaise, ketchup, and pickle relish in a small bowl.
Spread the mayonnaise mixture on 4 slices of the bread. Top with the Swiss cheese, beets, and sauerkraut. Top with the remaining bread, to form the sandwiches.
Melt ½ tablespoon of the butter in a large skillet over medium heat. Cook 2 of the sandwiches, covered and turning once, until the cheese is melted and the bread is golden brown, 3 to 4 minutes per side. Repeat with the remaining butter and sandwiches. (Reduce heat if the bread gets too dark before the cheese is melted.)
Serve the sandwiches with the salad.
How To Cook Beets
Scrub and trim the beets, leaving ½ inch of their roots and stems intact. Place in a pot with enough salted water to cover by 2 inches. Bring to a boil and simmer until tender, 30 to 45 minutes, depending on the size of the beets. (A paring knife should slide right in.)
How To Peel Beets
When the beets are cool enough to handle, use a paper towel to rub off the skins. The towel's lightly abrasive texture will make this messy job easier.