Add the cheese and sundried tomatoes to a food processor and pulse until chopped up. Add the scallions, parsley, basil, and nuts and pulse until it’s chopped up. Stream in the sundried tomato olive oil and pulse until combined. The pesto will be pretty chunky, but the pesto stays rolled up in the chicken better if it’s thicker.
Set your chicken breasts on a cutting board, and butterfly them with a very sharp knife, cutting into the thickest part of the breast. Then place the butterflied chicken breast into a gallon sized ziploc bag and pound it out with a meat mallet or a frying pan.
Before you get your hands messy, cut some kitchen twine to tie up your chicken. Lay the flattened chicken breast out on a flat surface, and season with salt and pepper. Spread a big spoonful of the sundried tomato pesto onto the breast, then roll the chicken up the length of the pieces, and secure with the kitchen twine. Repeat with the remaining chicken breasts and pesto.
Place the chicken on a sheet pan and bake for about 25 minutes, until the interior reaches 160 degrees F on an instant read thermometer. Let the meat rest for a couple minutes, then slice and enjoy!