I usually just use leftover tenderloin from this recipe, and have "grilled" them on the stove top with success.
1 large garlic clove, minced
Coarse salt and ground pepper
1 tablespoon vegetable oil, plus more for grates
1 pork tenderloin (3/4 to 1 pound)
1 large red onion, cut into 1/2-inch-thick slices
4 (10-inch or burrito-size) flour tortillas
4 tablespoons spicy brown mustard, plus more for serving
6 ounces thinly sliced baked ham
3 to 4 dill pickles, thinly sliced lengthwise
8 ounces provolone or Swiss cheese, coarsely shredded (about 2 cups)
On a work surface, sprinkle garlic with salt. Using the flat side of a chef's knife, draw the blade across the garlic mixture, repeating until a paste forms. In a small bowl, combine with 1/4 teaspoon pepper and the oil. Rub all over pork.
Heat grill to high; oil grates. Place pork on hottest part of grill; cover. Cook, turning occasionally, until an instant-read thermometer inserted in thickest part registers 155 degrees. 10 to 20 minutes. Let rest 5 minutes; thinly slice across the grain.
Meanwhile, place onion slices on cooler part of grill; cover. Cook, turning once, until soft and beginning to brown, about 10 minutes. Reduce grill to medium-low.
Spread 1 tablespoon mustard on each tortilla, leaving a 1/2-inch border. Dividing evenly, layer half of each tortilla with ham, pork, onion, pickles, and cheese. Fold tortillas; press to close.
Lightly oil grates. Place quesadillas on grill; cover. Cook, turning once, until browned in spots and cheese has melted, about 4 minutes. Cut into wedges; serve immediately.