1. Heat the oil in a skillet over medium heat. Add the shallots and cook until they begin to soften, about 2 minutes.
2. Turn the heat to medium-high, add the mushrooms and sauté 2 minutes more.
3. Add the tomatoes, tarragon, salt and pepper. Heat thoroughly. If using canned tomatoes, simmer for 30 minutes to reduce the acidic taste.
4. Adjust the salt and pepper to taste. (This can be made ahead and kept in the refrigerator for up to 2 days.)
For the Broiled Lamb Chops:
5. Preheat the broiler.
6. Season the lamb chops with salt and pepper.
7. Place the lamb chops on a broiler pan and broil 3 inches from the heat for 4 to 5 minutes. Turn and broil for an additional 3 minutes for medium rare, or 5 minutes for medium.
8. Serve the lamb chops with the mushroom ragout spooned over and around the chops.