In a small bowl, combine the celery, carrot, and both cheeses.
Butterfly the chicken breasts by starting at the thickest end, slice the breasts in half horizontally, carefully working away from you and toward the thinner end. You will end up with two thin chicken breast halves. Repeat with the remaining chicken breasts, leaving you with 6 total chicken breast halves.
Using a meat pounder, or the back of a frying pan, pound each chicken breast into even layer. Season both sides of each chicken breast with salt and pepper.
Divide the cheese mixture between each chicken breast. Spread the mixture over the chicken breasts, stopping about a 1/4 inch from the ends.
Roll the chicken breasts tightly starting at the widest end. Refrigerate for 15 minutes.
Prepare your breading stations. In a shallow dish, whisk egg and milk. In a second shallow bowl add the breadcrumbs, season with salt and pepper.
Coat each chicken breast roll in the egg mixture, followed by the breadcrumbs.
Coat air fryer with oil or cooking spray. Place the chicken breasts in the air fryer, ensuring they are not touching. Depending on the size of your air fryer you may want to cook the chicken in two batches.
Air fry at 375 degrees F for 15 minutes. Flip the chicken breasts and cook for another 5 minutes or until a thermometer reads 165 degrees F.
Combine melted butter and hot sauce. Brush over the cooked chicken. Serve with yogurt ranch.