Remove the leaves from the rosemary sprigs. Remove the skin from the garlic. Crush both with the salt and pepper. When all have been crushed almost to a paste, push this paste into each side of each lamb chop. Refrigerate for about 30 minutes to let the seasonings set in.

Preheat the oven to 200. Have ready a large skillet, with lid, that can hold all the lamb and is able to go into the oven. Have ready a large serving platter that can hold all the chops.

Heat the pan and add the olive oil. Put in the chops and sear them on both sides, about 3 minutes each. Put the pan in the oven, covered for about 10 minutes. Check that the meat is cooked to at least 125 degrees for rare. Remove the pan from the oven and put the chops on the serving platter. Cover to keep warm.

If there is a lot of liquid in the pan, pour most of it off. Return the pan to the stove and add the shallots. Sauté until they are translucent, then deglaze the pan with the red wine, scraping the bottom to get all the good bits up. Add the balsamic vinegar and let that cook down to about half. Add the butter and whisk it in, the sauce will thicken and take on a shiny appearance.