Directions

• Place 2 shallot halves in a mini food processor. Pulse until coarsely chopped, about three 1-second pulses. Add arugula, mint, and parsley; pulse until herbs are chopped, about five 1-second pulses. Transfer 1/2 of the herb mixture to a small bowl. Reserve remaining herb mixture for serving.
• Stir 4 tablespoons olive oil, 1 1/2 teaspoons salt, and 1/4 teaspoon black pepper into the bowl with the herb mixture; rub all over meaty parts of lamb. Prop the two lamb racks up together on a plate by placing the meaty ends on the surface with the bones upright, interlacing the bones so they rest against each other. Let sit at room temperature for 1 hour.
• Preheat the oven to 450 degrees F (230 degrees C) with racks in the upper and lower thirds. Line two large rimmed baking sheets with aluminum foil.
• Meanwhile, toss potatoes, carrots, and remaining shallot halves with 2 tablespoons olive oil, 1 teaspoon salt, and remaining 1/2 teaspoon black pepper in a large bowl. Arrange in an even layer on the prepared baking sheets.
• Roast vegetables in the preheated oven until beginning to brown and almost tender, about 15 minutes. Remove from the oven and combine onto one baking sheet. Set aside until ready to use. Do not turn the oven off.
• Once lamb has marinated, place lamb racks onto the empty baking sheet.
• Roast in the preheated oven for 10 minutes. Rotate the pan, scatter the roasted vegetables around the lamb, and continue to cook until a thermometer inserted into the thickest part of the lamb reads 125 degrees F (52 degrees C), 10 to 15 minutes longer. Remove from the oven and let rest for 10 minutes before slicing.
• Stir remaining 3 tablespoons olive oil, vinegar, red pepper, and remaining 1/2 teaspoon salt into the reserved herb mixture. Drizzle over lamb and vegetables.