A deli roast beef sandwich is a wonderful thing: a succulent tower of paper-thin slivers of rare red meat, perched on sliced seeded rye, slathered with mustard. Properly made, it threatens to be too tall to eat, but anyone with a firm grip will make the tender meat comply, squishing down just enough for that first juicy bite.

For me, making a roast beef sandwich at home is never quite the same. One reason is my glaring lack of an electric meat slicer to carve those skinny slices. But a bigger reason is the meat itself. At home, I layer leftover beef from the roast I served for dinner between bread for lunch the next day. Therein lies my biggest mistake.

That’s because the best cut for a cold roast beef sandwich is not the beef served hot from the oven. A hot slab of beef wants to be marbled with fat, so that fat can melt and baste the meat with all its richness and good flavor. Think of a rib roast: fatty, juicy and sublime.

But when that same meat is served cold, the fat solidifies into unpleasantly greasy white veins. What I usually end up doing is heating the meat to melt the fat. Which makes a great sandwich but is nothing like deli versions I crave.

The answer is to put the sandwich first and find the best cut of beef to serve cold, skipping the hot part of the bargain entirely.

Most delis roast lean cuts of meat, usually bottom, top or eye round from the cow’s rump, an economical choice. I tested all three, roasting them low and slow so they stayed juicy and rare. All made very fine sandwiches.

I would have happily stopped there, but the folks at Fleisher’s butcher shop suggested something else: a boneless top loin roast. Loin cuts are more expensive but a whole lot more tender, too, since the loin muscles are not as well-exercised as the cow’s behind.

The top loin roast came with a white cap of fat on top, which I left on for roasting so it could baste the meat; then I trimmed it off before slicing the cold meat into sandwich-thin slices.

It was mineral-tasting and brawny, terrifically tender and just lean enough for serving cold on seeded rye. Even better, unlike the round cuts, the loin was excellent eaten hot. Not that that was the point, but it certainly didn’t hurt.