Lamb Chops with Balsamic Vinegar

I adapted this recipe from one a person posted in a Craigslist forum. It’s amazingly simple and delicious. Even Mika thought the meat (sans the vinegar) was yummy. Mike really dug the vinegar, I thought it was good either way.
-6 lamb chops, trimmed
-salt & pepper
-1Tbsp olive oil
-herbes de provence
-1 large shallot, finely chopped
-1/3 cup balsamic vinegar
Sprinkle lamb chops with salt and pepper. Rub herbes de provence on both sides. Let stand for 15 minutes.
Heat olive oil over medium heat in a sautee pan and sautee lamb chops for about 3-4 minutes per side. You may have to do this in batches. Remove and keep warm.
Add the chopped shallot to the pan and sautee until tender. Add the vinegar, mix well and boil until the vinegar reduces by at least half. Return lamb chops to the pan, flip to make sure both sides are covered with the vinegar, and serve.