Cook the Chicken: Start by heating 1 tbsp olive oil in a large skillet over medium heat. Season 2 chicken breasts (cut into strips) with salt and pepper, and sauté them in the oil until golden brown and fully cooked through, which should take about 6-8 minutes. Add 2 cloves of minced garlic in the last minute of cooking, stirring until fragrant.
Prepare the Filling: In a mixing bowl, combine 1/2 cup mozzarella cheese, 1/2 cup cheddar cheese, 1/4 cup cream cheese, and 1/4 cup sour cream. Once the chicken is cooked, add it along with the garlic from the skillet to the bowl and mix well until everything is well combined.
Assemble the Wraps: Lay out the 2 large tortillas and spoon an even amount of the cheesy chicken mixture onto each tortilla. Roll them tightly, tucking in the corners as you go to secure the filling inside.
Heat & Crisp: Place the wraps seam-side down in the same skillet over medium heat. Cook for about 2-3 minutes on each side or until golden brown and crispy, and the cheese is melted. Alternatively, broil them in the oven for a few minutes, watching closely to avoid burning.
Garnish & Serve: Once cooked, remove the wraps from the skillet and let them sit for a minute. Slice in half, then sprinkle with 1 tbsp chopped fresh parsley. Serve with additional sour cream or salsa on the side for dipping.