Heat the oven to 450°. Oil an 8-by-11 1/2-inch baking pan or similarly sized gratin dish. In a large nonstick frying pan, heat 2 tablespoons of the oil over moderately low heat. Add the onions and cook, stirring occasionally, until translucent, about 5 minutes. Remove the pan from the heat and stir in the tomatoes and 1/4 teaspoon of the salt.
In a small bowl, combine the rosemary, thyme, 1/4 teaspoon of the salt, 1/8 teaspoon of the pepper, and the Parmesan. Spread half the tomato-and-onion mixture in the bottom of the baking dish; layer half the potatoes on top. Sprinkle half the Parmesan mixture over the potatoes. Repeat with the remaining tomatoes and onions, potatoes, and Parmesan. Cover the dish with aluminum foil and bake for 30 minutes.
Meanwhile, wipe out the frying pan and then heat the remaining 1 tablespoon oil in it over moderate heat. Sprinkle the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper over the lamb chops. Cook until browned, about 3 minutes per side. Remove the chops from the pan.
Remove the baking dish from the oven and remove the aluminum foil. Put the lamb chops on top of the potatoes and return the dish to the oven. Cook until the meat and potatoes are just done, 10 to 12 minutes longer.
Wine Recommendation: Bordeaux is the classic choice with lamb chops. Though our perceptions of Bordeaux are often distorted by the wildly expensive cru classé wines, many wines from the region are both affordable and delicious. Look for the appellations Bordeaux Supérieur, Bourg, Blaye, and Fronsac.
I added fresh garlic to the onions, and used garlic olive oil. Cooking the sweet onions down prevented the onions from overwhelming the dish. DH isn't a fan of onions but said they were fine in this dish. It was very mildly seasoned as written. If I made it again I would add more seasonings. I served it with steamed brocoli.
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