Step 1: Lightly grease the inside of a 6-quart (or larger) slow cooker with cooking spray.
Step 2: Place the chicken breasts or thighs at the bottom of the slow cooker.
Step 3: Pour the entire jar of salsa verde over the chicken.
Step 4: Distribute the cubed Velveeta cheese and the undrained can of Rotel over the chicken and salsa verde.
Step 5: Cover the slow cooker and cook on low for 6-8 hours, or on high for 3-4 hours, until the chicken is very tender and easily shreddable.
Step 6: Carefully remove the chicken from the slow cooker and shred it using two forks. Return the shredded chicken to the slow cooker and stir thoroughly to combine with the melted queso and salsa verde. The mixture should be thick, creamy, and well-coated.
Step 7: Heat a large non-stick skillet or griddle over medium heat. If desired, lightly spray with cooking oil.
Step 8: Place one flour tortilla in the hot skillet. Spoon a generous amount of the crockpot queso chicken filling over half of the tortilla. If using, sprinkle a little extra shredded cheese over the filling.
Step 9: Fold the other half of the tortilla over the filling to create a half-moon shape.
Step 10: Cook for 3-5 minutes per side, or until the tortilla is golden brown and crispy, and the cheese is fully melted and bubbly. The exact cooking time may vary based on your stove and skillet.
Step 11: Remove the cooked quesadilla from the skillet, place it on a cutting board, and slice it into wedges. Serve immediately.
Step 12: Repeat the process with the remaining tortillas and chicken filling. Serve hot with your favorite toppings like sour cream, guacamole, or extra salsa.