When you are dealing with very high end ingredients, it is more important than ever to let the product speak for itself.
At the restaurant, we rarely use Wagyu, but when we do it is fantastically simple: salt, fresh cracked black pepper. Sear and mark it on the grill, and finish in the oven. A little melted butter on it when it comes out, and that's all.
Do be aware that when you are cooking Wagyu (or, if you're very lucky, Kobe), you actually want to take it to at least medium rare, or even a little bit beyond. I know, that's heresy, and it's coming from a person who likes his steak cooked only to the point where a competent veterinarian could actually resuscitate it at the table. The reason is that when meat is as highly marbled as Wagyu (that is to say, when it has such a high distribution of intramuscular fats), you actually need to cook it further than a lean cut in order to melt the fat and extract all the flavour.
Beyond that, I would agree with Treblekicker. Practice on less-expensive steaks first. Learn how to really maximize the essential beefy flavour of a not-great steak; those lessons will make sure that as you move upwards in quality, you will be getting the most bang for your buck.
So for cooking steaks, a few guidelines:
- Medium is overdone. Seriously. Learn to love your steak red, there is a LOT more flavour
- Learn how to check for doneness by touch; cutting into the meat will release juices = losing flavour. To do this, hold up your left hand, palm facing you. Feel the pad at the base of your thumb. That is blue rare. Touch your forefinger to the tip of your thumb. That is rare. Do this sequentially with the rest of your fingers; that will be med-rare, medium, and well done in order. Well, that's North American colours; the French go slightly less for each level of doneness.
- There is conflicting advice on seasoning (salt and pepper) your steak. Thomas Keller maintains that meat should be seasoned 20 minutes before cooking and left to rest. Harold McGee (I think it was him) says that steaks should only be seasoned after they are flipped. I prefer seasoning before grilling, as the salt helps draw out some moisture which therefore assists in the Maillard reaction (browning and accompanying flavour development).
- Always let your steaks rest a few minutes after cooking. This redistributes juices throughout the meat. In practice, this means taking steaks off the grill or out of the pan a bit before they are done, as carryover cooking (residual heat) will continue to cook the meat.
- Only flip steak once. Try to keep an even cooking time on each side so that the inside cooks evenly. There is a caveat to this however! If you are cooking in a pan, frequent flipping (every 30 seconds or so) will create a much more evenly done steak, and bastes the meat in its own juices. This will come at the expense of slightly less browning, but will be significantly more tender. This is also the best technique for cooking hamburgers in a pan or on a flat-top grill.
- Never squish your steak with your tongs. This presses juices out of the meat.
That's all I can think of for now.
I've never used beef shin, but it's probably a good candidate for braising. Brown the outside in a pan, add aromatics (carrot, onion, celery, herbs) and beef stock, cover and let gently simmer for about 3 hours or so, until it starts to fall apart.
Once it's done, you can separate it from the juice and reduce the braising juices to a sauce that you can serve it with (you might add a bit of cornstarch slurry or a roux if you want to thicken the sauce more).
This basic technique works well for types of meat that have a lot of connective tissue.
Best Answer
Meat in stir-fries is often velveted. That makes for a supremely soft chunk of meat, and it can be done with any type of meat. This answer actually addresses chicken: How to cook extremely soft chicken?, but it applies just as well to beef. It's usually done with egg and cornstarch, but sometimes it's done with a small amount baking soda instead, as in this recipe for Beef and Broccoli.