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1
Prepare grill for cooking.
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2
Thread onions onto skewers (or put in grill basket), then brush with 1 tablespoon oil and season with salt and pepper.
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3
When fire is medium-hot (you can hold your hand 5 inches above rack for 3 to 4 seconds), grill onions, turning occasionally, until tender, 16 to 20 minutes.
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4
Transfer to a cutting board.
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5
When just cool enough to handle, cut onions into 1-inch pieces and toss with vinegar in a bowl.
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6
Season with salt and pepper.
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7
While onions are grilling, stir together the lime juice and remaining 3 tablespoons oil in a shallow dish, then add steak and marinate at room temperature, turning once, 10 minutes.
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8
Pat steak dry, then rub with chili powder, cumin, and coriander and season with salt and pepper.
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9
Grill steak on lightly oiled grill rack, turning once, 6 to 10 minutes total for medium-rare.
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10
Transfer to cutting board, then let stand 5 minutes before cutting diagonally into thin slices.
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11
While steak is standing, toast tortillas directly on grill rack, turning once, until puffed slightly and browned in spots, about 1 minute total.
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12
Serve steak, onions, cilantro, and salsa all wrapped in tortillas.
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13
Cook's note: If you aren't able to grill, onions (no need to skewer) and steak can be cooked in a lightly oiled well-seasoned ridged grill pan over moderately high heat and tortillas can be toasted over gas (hold with tongs) or directly on top of electric burners.
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14
Cut skirt steak into pieces to fit in grill pan and grill in batches without crowding.
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15
Preheat broiler.
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16
If using fresh tomatillos, remove husks and rinse under warm water to remove stickiness.
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17
If using canned tomatillos, drain and measure out 4 cups.
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18
Broil fresh tomatillos (do not broil canned), chiles, garlic, and onions on rack of a broiler pan 1 to 2 inches from heat, turning once, until softened and slightly charred, about 8 minutes.
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19
Peel garlic and pull off tops of chiles.
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20
Puree all ingredients in a food processor.
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21
Cook's note: Salsa can be made 1 day ahead and chilled, covered.
