Cooking meat medium-rare is different from cooking rare meat.
Simply put, it’s like cooking meat rare, and then leaving it to rest. Rare meat, like “Florentine steak”, is raw and bloody when you cut into it. Indeed, the trick to cooking a proper “Florentine steak” is removing the meat from the fridge at least 2 hours before cooking, in order to avoid having cold meat at the centre once cooked.
Both steak and beef fillet can be cooked medium-rare, but this technique is especially useful for cooking racks of lamb and duck breast.
If you cut into steak as soon as it’s cooked, you’ll see that it’s overcooked on the outside and raw on the inside. Moreover, a lot of blood will ooze out from the meat. If, instead, you let the meat rest at 70°-75°C for at least 20 minutes, you will cut into a perfectly cooked medium-rare steak. The liquids contained within the meat, which move to the centre during cooking, will instead uniformly spread to the entire surface of the meat while it rests, and no blood will come out of the steak when sliced.
The best way to cook a two-fingers high piece of steak or fillet is to start by searing it in an aluminium frying pan over medium heat for 5-6 minutes per side. After, place the meat in the oven preheated to 100° for 10 minutes, to prolong the cooking at low temperature. If you take it out immediately, the meat will still be rare, while if you let it rest for at least 20 minutes you will obtain medium-rare meat.
Contrary to beef, lamb rack and duck breast taste terrible if eaten rare. Here is where the empirical method comes in. After browning the meat for 3-4 minutes on each side, remove the pan from the heat and use a finger to test its consistency, which will fell jelly-like, especially in the centre. Place the pan in the oven preheated to 100° for 10 minutes, then prod the meat with your finger again. Give the meat another 5 minutes in the oven if its texture is still gelatinous. If instead it has reached a rubbery consistency, you can be sure that, after resting at least 20 minutes at 70° to allow the liquids to redistribute, your meat will be perfectly medium-rare.