This recipes comes from Lunch at the Shop by Peter Miller. Of the sandwich, Miller writes: "We do not have these very often -- the beef ends are usually easiest to find during the holidays, when the demand for the center cut is high and the tails are extra. It is a sandwich of good fortune." —Food52
At home: Heat a medium saucepan over low heat for a minute, then add the oil, butter, and onions. Stir well, add a good pinch of salt, and cover the pan. Sweat the onions for 20 minutes, stirring once. Uncover the pan, add the sugar, and stir. Cook, stirring frequently, for 25 minutes more. The onions will begin to stick a little and to brown. Add the vinegar, stir, and turn off the heat. Transfer the onions to a storage container, let cool, cover, and refrigerate.
At the shop: Let the tenderloins and browned onions warm up to room temperature.
In a small bowl, mix the horseradish and mayonnaise together, and then stir in the mustard. Add a squirt of lemon juice, stir, and set aside.
Slice the tomato into 8 slices and lightly salt the slices.
Slice the rolls and spread some of the horseradish mayonnaise on one cut side of each. If you have any sauce from the roasted tenderloins, mix that with the butter, and spread the mixture on the other cut side of each roll; otherwise, simply butter the side.
Lay several tenderloin pieces over the horseradish mayonnaise on each roll, slightly overlapping them. Add a little salt and a good grind of pepper. Add 1 Bibb leaf, 2 tomato slices, and a good forkful of the browned onions to each sandwich. Squeeze a little lemon over the onions and close the rolls. Cut each sandwich in half so the layers can be seen, and serve with something fresh, such as peeled carrots or a radish.