In a large skillet set over medium heat, heat 1 tbsp of olive oil and then add the onion; cook until softened and slightly caramelized, about 2-3 minutes
Add the spices and stir well, then add the shredded chicken and stir to coat well.
Stir in black olives, corn kernels and water and cook until heated all the way through, about 2 minutes. Set aside.
Place a medium skillet over the heat source and add a teaspoon or so of oil to it. Add 1 flour tortilla, sprinkle with about one quarter of the shredded cheese, then top with half of the chicken mixture, followed with another sprinkle of cheese and finally, cover with a second tortilla and press it down firmly.
Cook for a few minutes, until golden brown on the bottom and carefully flip the quesadilla over to cook the other side until golden brown.
Remove the finished quesadilla to a plate and repeat this entire process to make a second quesadilla with the remaining ingredients, then slice and serve with some salsa and sour cream, if desired.