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1
Stir together garlic, onion, mint, savory, olive oil, lemon zest and juice, and cumin in a baking dish just large enough to hold lamb.
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2
Put lamb in dish and turn to coat, rubbing marinade into entire surface.
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3
Marinate lamb, covered and chilled, turning once or twice, at least 12 hours.
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4
Mash garlic to a paste with kosher salt using a mortar and pestle (or mince and mash with a large heavy knife), then add 1 cup mint and pound to a paste (or mince and mash with knife).
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5
Transfer to a bowl and whisk in yolks, then add half of oil, 1 to 2 teaspoons at a time, whisking constantly.
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6
Whisk in lemon juice, then slowly add remaining oil, whisking.
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7
Season with salt and pepper and stir in warm water.
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8
Working with several leaves at a time, stack remaining cup mint leaves, then roll up and thinly slice crosswise to make a chiffonade (thin strips).
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9
Stir mint into aioli and chill until ready to use.
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10
Preheat oven to 400F.
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11
Wipe all of marinade from lamb and discard.
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12
Pat lamb dry and season both sides generously with salt and pepper.
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13
Arrange lamb, boned side up, on a work surface and, beginning with a long side, roll up as tightly as possible and tie tightly with string.
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14
Heat vegetable oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then brown lamb on all sides, about 8 minutes.
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15
Transfer to rack set in roasting pan and roast in middle of oven until an instant-read thermometer inserted into lamb reads an average of 140F for medium-rare (test in several places, as different muscles cook at different speeds; temperatures should range from 120 to 160F), 40 to 60 minutes.
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16
Let stand 15 to 20 minutes before slicing.
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17
Serve lamb with aioli.
