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Preheat oven to 400°F with rack in middle.
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Mince and mash garlic to a paste with 1/2 tsp salt and 1/2 tsp pepper. Stir together with herbs and 1 Tbsp oil.
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Put tomatoes cut sides up in an oiled small baking dish and drizzle with a third of garlic mixture. Roast until tender, 30 to 40 minutes.
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Meanwhile, pat lamb dry and season with 1/4 tsp salt and 1/4 tsp pepper.
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Heat 1 Tbsp oil in a 10-inch ovenproof skillet over medium-high heat until it shimmers. Brown lamb on all sides, 4 to 6 minutes total. Transfer lamb to a cutting board and discard oil from skillet.
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Heat remaining Tbsp oil in skillet over medium heat and cook shallots and potatoes, stirring occasionally, until edges are browned, 3 to 5 minutes. Stir in water and half of remaining garlic mixture and remove from heat.
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Rub remaining garlic mixture on fat side of lamb racks. Arrange lamb over potatoes and roast in oven until an instant-read thermometer inserted into center of meat (do not touch bone) registers 130°F for medium-rare, 20 to 25 minutes.
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Let stand, loosely covered, 5 to 10 minutes. Serve with tomatoes.