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1
Stir together yogurt, garlic, rosemary, and pepper in a 13- by 9-inch glass baking dish or 2-gallon sealable plastic bag.
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2
Add lamb, turning to coat completely, and marinate, covered and chilled, turning over once or twice, 5 hours.
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3
Bring lamb to room temperature, about 1 hour.
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4
Remove lamb from marinade, discarding marinade, and put on a work surface.
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5
Run skewers horizontally through meat, about 1 1/2 inches apart, first lengthwise (4 or 5 skewers), then crosswise (4 or 5 more) to form a grid.
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6
(Skewering makes meat easier to move and turn over.)
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7
Sprinkle with kosher salt.
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8
Prepare grill for cooking.
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9
If using a charcoal grill, open vents on bottom of grill, then light charcoal.
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10
Charcoal fire is medium-hot when you can hold your hand 5 inches above rack for 3 to 4 seconds.
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11
If using a gas grill, preheat burners on high, covered, 10 minutes, then reduce to moderate.
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12
Grill lamb, covered only if using a gas grill, on lightly oiled grill rack, turning occasionally, until thermometer inserted diagonally into thickest part of meat registers 125F for medium-rare (thinner parts will register higher), 25 to 30 minutes if using charcoal or 20 to 25 minutes if using gas.
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13
Transfer lamb to a cutting board and let stand 10 minutes before thinly slicing.
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14
Stir together rosemary and sea salt and serve with lamb.
