I saw the son of Lydia Bastianich do this on one of those PBS cooking shows:
take a thick steak, grill it super hot until it is charred on the outside but only 100 degrees F (i.e. still blood raw) interior, tent it with foil, and let it sit 20-30 minutes until it is room temp.
I like this TV show, because the end result they display on-camera is the exact dish prepared on the air. For this dish, they sliced it and it was the most perfectly medium rare I have ever seen. I was flabbergasted.
So, the first time I got good quality steaks, I tried it. It worked (halleluiah); I eat meat 7 days a week, and this was one of the best beef dishes I have ever had. We got 1 inch porterhouses. I sliced off the filet piece, leaving the bone attached to the NY strip (called shell steak back East). I prepared both cuts separately. Both turned out great.
Well, OK, I stuck a huge chunk of butter on the meat before resting. At the end of the allotted time, I sliced the meat into bite sized pieces, drizzled the melted butter on top, and sprinkled that chunky, expensive ($20 for a 8 oz jar) sea salt on top. Interesting side note: there were NO meat drippings on the plate, only melted butter. So, there is really no need for a pan sauce, since all of the meat juices stayed in the meat where they belong. Butter and sea salt where the only flavorings, and this was all the meat needed for great taste.