For most families, Sunday roast beef isn’t prime rib; it’s a lesser cut that’s sometimes good, sometimes not. The roasts my parents prepared throughout my childhood were typically tough and dried out and better suited for sandwiches the next day. But when my grandfather was at the stove, he could take the same inexpensive cut and turn it into something special—tender, rosy, beefy-tasting meat that had everyone asking for seconds. I wanted to work the same kind of wizardry on my own Sunday roast.

First I needed to zero in on the most promising beef. After a week in the kitchen testing a slew of low-cost cuts, I had a clear winner: the eye-round roast. Though less flavorful than fattier cuts from the shoulder (the chuck) and less tender than other meat from the back leg (the round), my eye roast had one key attribute the others lacked: a uniform shape from front to back. This was a roast that would not only cook evenly but look good on the plate as well.

My next challenge was choosing between the two classic methods for roasting meat—high and fast or low and slow. I began with the more common high-heat approach, quickly searing the meat on the stovetop and then transferring it to a 450-degree oven for roasting. The technique works great with more upscale rib and loin cuts but showed its flaws with the leaner eye round, yielding meat that was overcooked and dried-out.

But before heading down the low-temperature path, which normally involves roasting meat in an oven set between 250 and 325 degrees, I wanted to try something more extreme. To extract maximum tenderness from meat, the popular 1960s nutritionist Adelle Davis advocated cooking it at the temperature desired when it was done. For a roast to reach an end temperature of 130 degrees for medium-rare, this process could involve 20 to 30 hours of cooking. Davis’s advice wasn’t new. Benjamin Thompson, the 18th-century physicist who invented the roasting oven, observed that leaving meat to cook overnight in an oven heated by a dying fire resulted in exceptional tenderness.

Tossing aside practical considerations like food safety and the gas bill, I decided I had to replicate these two experts’ findings. I set the one oven in the test kitchen capable of maintaining such a low temperature to 130 degrees and popped in an eye round. Twenty-four hours later, I pulled out a roast with juicy, meltingly tender meat that tasters likened to beef tenderloin. What special beef magic was going on here?

When I thought back to the test kitchen’s discoveries, I had my answer: Beef contains enzymes that break down its connective tissues and act as natural tenderizers. These enzymes work faster as the temperature of the meat rises—but just until it reaches 122 degrees, at which point all action stops. Roasting the eye round in an oven set to 130 degrees allowed it to stay below 122 degrees far longer than when cooked in the typical low-temperature roasting range, transforming this lean, unassuming cut into something great.

But given that most ovens don’t heat below 200 degrees—and that most home cooks don’t want to run their ovens for a full day—how could I expect others to re-create my results? I would have to go as low as I could and see what happened. To accommodate the widest possible range of ovens, I settled on 225 degrees as my lowest starting point. I also decided I would brown the meat first to give it nice color and a crusty exterior. (While tender, my 130-degree roast had an unappetizing gray exterior.) Searing would also help to ensure food safety, since bacteria on roasts are generally confined to the outside.

When I took the roast out of the oven, however, I was disappointed. It was tender, but nothing like the texture of the eye round cooked at 130 degrees. What could I do to keep the meat below 122 degrees longer? A new idea occurred to me: Why not shut off the oven just before the roast reached 122 degrees? As the oven cooled, the roast would continue to cook even more slowly.

Using a meat-probe thermometer to track the internal temperature of the roast, I shut off the oven when the meat reached 115 degrees. Sure enough, the meat stayed below 122 degrees 30 minutes longer, allowing its enzymes to continue the work of tenderizing, before creeping to 130 degrees for medium-rare. Tasters were certainly happy with this roast. It was remarkably tender and juicy for a roast that cost so little.

With the tenderness problem solved, it was time to tackle taste. So far I’d simply sprinkled salt and pepper on the roast just before searing it. Perhaps the flavor would improve if the meat were salted overnight or even brined. Brining—normally reserved for less fatty pork and poultry—certainly pumped more water into the beef and made it very juicy, but it also made it taste bland, watery, and less beefy. Next I tried salting the meat for first four, then 12, and finally 24 hours. As might be expected, the roast benefited most from the longest salting. Because the process of osmosis causes salt to travel from areas of higher to lower concentration, the full 24 hours gave it the most time to penetrate deep into the meat. There was another benefit: Salt, like the enzymes in meat, breaks down proteins to further improve texture.

At last I had tender, flavorful beef for a Sunday roast that even my grandfather would have been proud to serve to his family. The leftovers—if there were any—would have no need for mayonnaise or mustard to taste good.