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1
Place the unpeeled garlic clove on a cutting board, and smash with the flat side of a knife blade.
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2
Peel off the papery skin and discard; trim away the root end.
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3
Holding the tip of the blade steady on the cutting board with your free hand, and rocking the base of the blade back and forth, chop the garlic into coarse, even pieces.
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4
Gather the chopped garlic in a pile; sprinkle generously with coarse salt.
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5
Place the flat side of the knife blade on top; press firmly, pulling the knife toward you.
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6
Repeat until a paste forms.
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7
In a small bowl, combine with 1/4 teaspoon pepper and the oil.
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8
Rub all over the pork.
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9
Heat the grill to high; oil the grates.
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10
Place the pork on the hottest part of grill; cover.
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11
Cook, turning occasionally, until an instant-read thermometer inserted in the thickest part registers 155F, 10 to 20 minutes.
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12
Let rest for 5 minutes; thinly slice the pork across the grain.
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13
Meanwhile, place the onion slices on the cooler part of the grill; cover.
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14
Cook, turning once, until soft and beginning to brown, about 10 minutes.
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15
Reduce the grill to medium-low.
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16
Spread 1 tablespoon of the mustard on each tortilla, leaving a 1/2-inch border.
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17
Dividing evenly, layer half of each tortilla with the ham, pork, onion, pickles, and cheese.
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18
Fold the tortillas; press to close.
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19
Lightly oil the grates again.
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20
Place the quesadillas on the grill; cover.
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21
Cook, turning once, until browned in spots and the cheese has melted, about 4 minutes.
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22
Cut into wedges; serve immediately with additional mustard.
