Remove your beef from the refrigerator and allow to temper for a least a half hour before cooking. Season liberally with salt and pepper.

Meanwhile, place the tomatoes on a wire rack over a sheet tray. Drizzle with the olive oil and season with salt and pepper. Scatter half of the thyme and savory sprigs over the top of the tomatoes. Roast in a hot wood oven, rotating once, until soft, about 6-10 minutes depending on your tomatoes and oven temperature. Remove from the oven and allow to cool. When cool enough to handle, discard the herb sprigs and remove the skins from the tomatoes. You should be able to peel them right off with your fingers.

Preheat a large roasting pan or skillet in a very hot wood oven. Add the vegetable oil – it should smoke. Place the steaks in the pan, slide the pan back into the oven, and seal up the oven. Allow the steaks to roast for 4-5 minutes. Remove the oven door and turn the steaks. Scatter the remaining savory and thyme over the steaks and roast for 2-3 minutes more. Add the butter to the pan; when melted, baste the steaks with the hot fat for 1 minute. Cooking times will vary depending on your oven temp and the thickness of your steaks – listed here are the approximate times for this particular session, with the meat cooked to medium rare.

Remove the meat from the roasting pan. Cut your cheese into wedges and top each steak with a piece. Allow to rest for 5-7 minutes, then serve with the roasted tomatoes alongside.