In a large skillet, heat the olive oil over medium-high heat. Add the bite-sized chicken pieces and season with salt and pepper. Cook for about 5 minutes, stirring occasionally, until the chicken is browned.
Sprinkle the taco seasoning over the chicken. Stir to coat the chicken evenly, and cook for another 2-3 minutes. Add garlic and stir until fragrant.
Sprinkle the flour over the chicken and stir to combine. Pour in the chicken stock gradually, stirring constantly until the mixture thickens and the chicken is cooked through. Remove from heat.
Lay out four tortillas on a clean surface. Evenly distribute the chicken mixture, followed by a generous amount of cheddar cheese, chopped scallions, green chiles, and a drizzle of green enchilada sauce. Top with the remaining tortillas.
In the same skillet, heat a tablespoon of vegetable oil over medium heat. Carefully place one quesadilla in the skillet and cook for 3-4 minutes on each side, or until golden brown and crispy. Repeat with the remaining quesadillas, adding more oil as needed.
Cut the quesadillas into wedges and serve warm with a side of restaurant-style salsa and sour cream. Enjoy the smiles and satisfaction as everyone digs in!