Marinade chicken: In medium bowl, whisk egg, lemon juice, minced garlic, parsley, salt & pepper. Place chicken in marinade to cover. Place in refrigerator for 30 minutes.
In shallow bowl mix panko crumbs and parmesan cheese.
Preheat oven to 400 degrees.
Take chicken out of marinade and dredge in crumb mixture.
Lay chicken on a prepared baking sheet pan (lightly greased).
Arrange cut potatoes around chicken.
Mix butter, garlic and salt & pepper in a small bowl. Pour 1/2 the mixture over potatoes.
Bake for 15-20 minutes, until lightly golden.
Remove from oven and flip chicken over. Add zucchini and squash. Pour remainder butter mixture onto vegetables.
Place oven on broil. Place pan back in oven for an additional 10 minutes, until chicken reaches internal temperature of 165 degrees.