In a skillet over medium heat, add olive oil, shredded rotisserie chicken, cream cheese, paprika, garlic powder, salt, and black pepper. Stir until the chicken is warmed through and the cream cheese is fully melted and combined.
Remove from the heat and stir in parsley, green onion, and a squeeze of fresh lemon juice.
Place 3 tortillas on a clean surface. Sprinkle each with cheese, then divide the chicken mixture evenly over the cheese.
Add more cheese on top of the chicken, then place the remaining 3 tortillas over the filling to close each quesadilla.
Lightly butter the outside of the tortillas, then cook in a panini press until the quesadillas are golden and crisp and the cheese is melted, about 3–5 minutes.
Alternatively, cook in a skillet over medium heat, lightly buttering the outside of the tortillas and flipping carefully once until both sides are golden and crisp.
Let rest for 1 minute before slicing and serving. Bon appétit.