In a shallow plate or zip-top bag, combine 2 tablespoons of the olive oil, the crushed red pepper, sliced garlic, and a sprig of rosemary.
Add the sirloin and coat well with the marinade.
Allow it to sit at room temperature for 20 to 30 minutes or up to 8 hours in the refrigerator.
Heat the oven to 250 degrees Fahrenheit.
Add the remaining 2 tablespoons of olive oil, the halved garlic cloves, and the remaining rosemary to a sauté pan just large enough to hold the steaks.
Remove the meat from the marinade and season it with salt and pepper.
If you have a grill on your stove, grill the steaks just so the exterior of the meat is nicely browned (brown all sides if using a thick square of meat).
If you don’t have a grill, sear the meat in a heavy-based sauté pan (not the prepared one) over medium-high heat.
Take the meat off the grill or out of the pan before the interior starts to cook.
The entire browning process should last about 4 minutes for a thick cut of beef and a little less for thinner cuts.
Transfer the meat to the prepared sauté pan and cook in the oven, basting the meat with the olive oil every 4 minutes or so, until the meat is cooked to your liking.
We serve ours medium rare (about 103 degrees Fahrenheit on a meat thermometer), and it usually takes 18 minutes.
A thinner cut will take less time; begin checking at 12 minutes.
Transfer the steaks to a cutting board and stir together the meat juices and olive oil that remain in the pan.
Let the meat rest for a couple of minutes to allow the interior juices to redistribute and then slice the steaks across the grain 1/4 inch thick.
Arrange the slices on the heated plates.
Drizzle some of the juices from the pan over the slices, sprinkle with a pinch of sea salt, and top with shavings of Parmigiano-Reggiano.