Heat olive oil in a skillet over medium heat.
Add minced garlic and sauté until fragrant, about 1-2 minutes.
Add the cooked diced chicken breast to the skillet and season with salt and black pepper.
Stir to combine and heat through for 3-4 minutes.
Remove from heat and mix in shredded mozzarella and cheddar cheeses, letting them melt slightly.
Warm the flour tortillas in a separate pan or microwave until pliable.
Spread a small amount of butter in a skillet over medium heat.
Place each tortilla in the skillet, add a generous portion of the chicken and cheese mixture in the center.
Fold the sides and roll the tortilla into a wrap.
Cook each wrap in the buttered skillet for 2-3 minutes on each side until golden brown and cheese is melted inside.
Remove from heat, sprinkle with chopped parsley if desired, and serve immediately.