Preheat oven to 350 F. Trim all visible fat and tendons from chicken breasts. Put chicken breasts, one at a time, inside a heavy plastic plastic freezer bag and pound with meat mallet or other heavy object until 1/4 inch thick.

Put pesto, goat cheese, and chopped basil in food processor and buzz a few times until mixture is combined but not completely blended. Spread 1/6 of pesto/basil/goat cheese mixture on each chicken breast. Roll up chicken, starting with smallest end, tucking in loose pieces and securing with two toothpicks.

Put flour, beaten egg, and bread crumbs combined with parmesan cheese into three separate flat dishes. Roll each chicken breast, first in flour, then in egg, then in bread crumb/parmesan mixture.

Spray glass casserole dish with nonstick spray and arrange chicken so pieces are not touching. Bake at 350 F for about 50-60 minutes, or until chicken is slightly browned and firm, but not hard to the touch. I recommend you start checking it after 40 minutes, and remove from oven as soon as the chicken feels firm and is slightly browned.