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1
Preheat your grill to medium-high (about 400-450 F). Oil the grates of the grill (I use paper towels and hold them with tongs.)
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2
In a wide, shallow dish, combine the chili powder, parsley, olive oil, lime juice, salt, cumin and red pepper flakes. Whisk to combine. Add the chicken to the wet rub, turning to coat. Place the chicken on the preheated grill and cook for about 6-7 minutes per side, or until cooked through (the chicken should register about 165 F on an instant read thermometer). Transfer the chicken to a plate and let rest for 5-10 minutes, then shred into bite-sized pieces. Cook the onions until softened and golden brown either by using a grill basket or by threading the onions on a skewer, brushing well with olive oil and placing directly on the grill grates. (You could also cook the onions on the stove top in a skillet, if you prefer). Maintain grill temperature.
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3
Put the tortillas on a plate, cover with a damp paper towel and microwave for about 25 seconds to make them pliable - you may want to do this in batches as you assemble them. Brush one side of the tortilla with olive oil. Place the tortilla oiled side down on your work surface, and top half of the tortilla with the chicken, tomato, and onion. Fold the tortilla in half to cover the filling. Repeat to use remaining filling and make as many quesadillas as desired.
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4
Oil the grill grates one more time then place the assembled quesadillas on the grill. Cook until the tortillas are browned on the outside - about 2 minutes per side. Slice into wedges and serve with sour cream, salsa, guacamole, or your favorite toppings.
