I think impatience may be the issue partly. Will try that next time, but what temperature for the oven and for how long? Fan-forced or with elements top and bottom. I can experiment. Just not in the mood for all the youtube videos and clickbait on this topic and there may be a simple answer here which someone knows. But that is probably it, 2 minutes either side then cast iron pan uncovered (?) into an oven.
The restaurant steak was just juicy all the way through whereas mine was dried out most of the way through and burned on the outside surfaces.
For oven temp: something in the range of 425ºF, it's not critical.
The idea is to sear just long enough to get the browning which gives it flavor, but not so long that the high heat starts to cook the steak unevenly from the outside in. The ideal is to have a seared outside with a nicely even red/pink cross-section.
The steak will cook more evenly in the oven than in the pan, so that's where you want to do the majority of your actual cooking. Note that this technique is actually easier with thicker steaks, since they will not overcook in the pan.
The sear should look something like this:
When it comes to the inside, you want this:
Not this:
There's another technique you can try, which is called the reverse sear. A lot of restaurants and professional chefs use this technique. It's the exact reverse - you first cook the steak to a perfect juicy red/pink inside in the oven, and then finish by searing quickly on the stove.
This is a foolproof way to get a perfect inside. The downside of the reverse sear technique is you don't get as many nice browned bits left behind in the pan (called "fond"), which are the starting point for a delicious deglaze or pan sauce like the peppercorn sauce you had.
Either cooking order will give you a delicious result with a bit of practice.
As far as how long: the answer is, until it's done. If you want it to look like the second picture above, which is roughly medium rare, the perfect internal temperature is 125ºF. The easiest and most aesthetic way to gauge this is with an instant read digital thermometer, which are like $10 on Amazon. But in a pinch, you can also cut into the meat and see what the inside looks like. Keep in mind meat keeps cooking after you take it off the heat - its internal temperature may rise as much as 5º after taking it off the heat - so you should take it off just a smidge before it hits the temp or color you want. (If you reverse sear, you should take it out of the oven even sooner - about 15º before the target temp, because it will cook more while you're searing it.)
A note on steak quality: it's important. Nice restaurants generally have access to a higher grade of steak than what you'll find packaged in your local supermarket, which is part of why they're more flavorful. If you want a restaurant-quality steak, it may be worth going to Whole Foods, which tends to have good meat, or, even better, a local butcher.
One last note. Whether you do it before or after the oven, the absolute most important part of searing a steak is to pat it
completely dry with paper towels. If there's any moisture on the outside of the steak, it will not sear properly because the water will steam when it touches the hot oil, creating a barrier that prevents heat transfer from the oil to the meat.
For the same reason, if you salt before cooking, it should be immediately before you put the steak in the pan. If you wait 5 minutes, the salt will draw water out to the surface of the steak and you will have to pat it dry again.
Here are a few links that have very good information:
The reverse sear is one of the easiest and arguably best methods of cooking a steak. Start it in a low oven, then quickly sear it in a hot pan or on the grill for a beautiful crust.
www.seriouseats.com
We put to rest seven of the most stubborn myths about grilling steaks, including that you should let your steak rest at room temperature beforehand and that you should only flip steaks once.
www.seriouseats.com