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1
Place the olives in a food processor fitted with a steel blade and pulse until finely chopped.
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2
Transfer the olives into a small mixing bowl and add the garlic, parsley, 1 tablespoon of the olive oil and the vinegar.
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3
Stir well and set aside.
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4
Preheat the oven to 150 degrees F and line a baking sheet with heavy-duty aluminum foil.
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5
Heat a 12-inch skillet over medium heat.
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6
Place 1 tortilla in the skillet and cook for 1 1/2 minutes, or until soft and puffed slightly at the edges.
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7
Flip the tortilla with tongs and cook for 1 to 2 minutes, or until browned and puffy.
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8
Repeat with the remaining tortillas.
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9
Layer 1 slice each of mortadella and ham, 2 slices of salami, and 1 slice of provolone on half of each tortilla.
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10
Top with one-sixth of the olive salad.
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11
Fold the tortillas over the filling and press them closed with the palm of your hand.
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12
Brush the tortillas on both sides with the remaining olive oil and sprinkle them lightly with salt.
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13
Return the skillet to the stove and heat it over medium-high heat.
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14
Add 2 of the quesadillas and toast them for 1 to 2 minutes, or until the bottoms are crispy and brown.
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15
Turn the tortillas gently, and toast the other side.
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16
Place the cooked quesadillas on the baking sheet and keep them warm in the oven while cooking the remaining 4 quesadillas.
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17
To serve, cut each quesadilla in half.
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18
The quesadillas can be assembled before cooking 1 day ahead and refrigerated, separated by layers of plastic wrap.
