Cuts of meat that do well with fast cooking include cuts from the rib, and sometimes the shoulder. (The only exception to this is top-of-the-rib roast, which needs to be cooked low and slow.)
The first sauce is a gremolata, and it gets spooned over meat, or is eaten alongside it, almost like a relish. The pan sauce is served alongside the meat as well.
Take your choice between the two of them!