In a small bowl, combine minced garlic, smoked paprika, cumin, salt, and pepper to create a flavorful spice rub for the chicken filling.
Heat a skillet over medium-high heat and add a splash of olive oil; cook the shredded chicken until heated through and slightly crispy at the edges, about 3-4 minutes. Remove from pan and set aside.
Wipe out the skillet and add a little more oil if needed. Place one tortilla on the skillet and sprinkle evenly with shredded cheese, then layer the warm chicken on top. Top with another sprinkle of cheese, then cover with a second tortilla.
Cook the quesadilla over medium heat until the bottom is golden brown and crispy, about 2-3 minutes. Use tongs or a spatula to carefully flip it over and cook the other side until equally golden and the cheese is melted.
Remove the cooked quesadilla from the skillet and let it rest for a minute; then use a sharp knife to cut it into wedges.
Repeat the process with remaining tortillas, chicken, and cheese until all are assembled and cooked.
Serve the quesadillas hot and crispy, with your favorite salsa, sour cream, or other toppings if desired.
