Start by blending the salt, smoked paprika, garlic powder, oregano, and cumin in a small bowl. Sprinkle the seasoning mixture generously over the chicken, ensuring even coverage on all sides.
In a large nonstick skillet, heat 1½ tablespoons of olive oil over medium-high heat until the oil shimmers. Place the seasoned chicken strips into the skillet and cook undisturbed for 2 to 3 minutes until golden brown. Flip the chicken pieces, reduce the heat to medium, and continue cooking for another 3 to 4 minutes until fully cooked. Once done, transfer the chicken to a plate or cutting board.
Pour the salsa and water into the same skillet, stirring to combine the flavors left behind from the chicken. Let the mixture simmer uncovered over medium-low heat for about 7 to 9 minutes, or until it thickens and most of the liquid has evaporated.
While the sauce is simmering, use two forks to shred the chicken into small, bite-sized pieces. Once the sauce reaches a thick consistency, remove it from the heat if the chicken isn’t ready. Stir the shredded chicken, along with any juices from the plate, into the sauce until evenly coated. Scoop out half of the chicken mixture and save it in a container for future use (refrigerate or freeze as needed).
Clean the skillet and return it to the stove. Add ½ tablespoon of oil over medium heat. Place one tortilla into the skillet, pressing gently to swirl it around and evenly coat the bottom with oil. Evenly sprinkle ¾ cup of shredded cheese across the surface of the tortilla, leaving about a ½-inch border around the edges. Spread approximately ⅓ cup of the chicken mixture over one half of the tortilla.
Allow the cheese to melt slightly, then fold the tortilla in half to form a crisp half-moon shape. Continue cooking for 1 to 2 minutes on each side, or until the tortilla is golden brown and crispy and the cheese has melted completely. Adjust the heat as necessary to avoid burning.
Repeat this process with the remaining oil, tortillas, cheese, and chicken mixture. If needed, lightly cover the prepared quesadillas with foil to keep them warm. Once all the quesadillas are ready, allow them to rest briefly to firm up the filling.
Slice each quesadilla into wedges and serve with sour cream and lime wedges on the side for a fresh, tangy finish.