I'll often do what my mom referred to as 'planned overs', and make too large of a roast for us to eat, then turn the rest into a stew or something else in the following nights.
The only comment I really have is that if you like the 'fall apart tender', I find it more difficult to get the second time around. I recall that Alton Brown specifically cooked the meat ahead of making a stew in an episode of Good Eats, and in checking the transcript of the episode, he said it's due to the behavior of gelatin:
You can see that the meat is very, very soft. It’s almost like pulled pork in there. We’ve had complete collagen to gelatin conversion. But when this cools for an hour, and if we refrigerate it after that, we’ll see that this is going to change. More on that later.
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Now, what’s really interesting, though, is that once gelatin has reached the gel state, it takes more heat to re-dissolve it than it did to render it from collagen in the first place. And, believe it or not, that is a good thing
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Ahh, the meat is perfectly heated through, but it’s not falling apart. That’s because we let it cool down before reheating, and that is why stews, braises, fricassees, and blanquettes are always better the second day.
The only mistake you made was the choice of cut, and maybe the quality of the beef itself. Round (in the UK/AU/NZ topside and silverside) is from the rear end of the animal, and is a working cut. Working cuts have to exert a force, so the muscle must have lots of collagen to distribute the force from the tendon throughout the muscle. Collagen is a tough material which breaks down in the presence of heat and moisture, not just heat, so working cuts make poor roasts or steaks and are better braised or stewed.
The upside to working cuts is that they have a stronger flavor, and the collagen when broken down by moisture turns to gelatin which adds to the flavor and mouth feel. A well-prepared braised piece of beef is as good as a roast any day in my opinion. It's also better value, round and other working cuts are much cheaper than tender cuts.
Your technique as described is perfect, and if you'd chosen a rib, short loin, or sirloin roast (US cuts) it would have come out beautifully. Where you erred was at the store when you chose a working cut for roasting.
Now some people on the forum are probably preparing a rebuttal at this point saying "you can roast round and have it be tender", and they'd be right up to a point. The best quality beef is reared and slaughtered better, so if you bought US Prime round it has a good chance of coming out relatively tender, however it's hard to find. My assessment would be for what you'd find in the average store in the US, which is Choice grade. Choice encompasses something like 75% of beef produced, so has a huge range of quality.
You can tell a lot about meat by touching it. Stick your fingers in it, if they go in easy and the meat springs back then you have a tender cut, if you can't get your fingers in it it's a braising cut. If you stick your fingers in and the meat doesn't spring back its old, so don't buy it.
Best Answer
Topside is a good cut of beef for slowly braising, which is what you're doing here. I assume you're following a recipe that calls for 2 hours of cooking? Many recipes for braised meat dishes tend to understate the amount of time it needs to be cooked to become tender (just like how they will tell you you can caramelise onions in 20 minutes). 2 hours is a very short time for this kind of dish. I tend to cook braised beef for anywhere between 4 and 6 hours to get it tender enough to fall apart. It takes time for the chemical reactions that you're after to take place. Give it at least another two hours, and it will be much better.