Preheat oven to 200°C | 400°F. Lightly grease a baking tray / sheet with cooking oil spray, or a light coating of oil. Set aside.
In a large bowl, whisk together the egg, lemon juice, 2 teaspoons garlic, parsley, salt and pepper.
Dip chicken into egg mixture, cover and allow to marinade in the refrigerator for 30 minutes to an hour (if time allows).*
In another bowl, combine the breadcrumbs with the parmesan cheese.
Dredge the egg coated chicken in the breadcrumb/parmesan mixture, lightly pressing to evenly coat.
Place chicken onto the baking sheet / tray and lightly spray with cooking oil spray. Arrange the potatoes around the chicken in a single layer. Mix together the butter, 2 teaspoons garlic and salt to taste, and pour half of the butter mixture over the potatoes. Toss to evenly coat.
Bake in preheated oven for 15 minutes.
Remove baking tray from the oven and carefully flip each chicken breast. Move the potatoes to one side and place the green beans around the chicken on the other side of the baking sheet. Pour over the remaining garlic butter and return to the oven to broil (or grill) on medium-high heat for a further 10 minutes, or until chicken is golden and crisp, and potatoes are cooked through.
Sprinkle with fresh chopped parsley (optional), and serve immediately.
*The chicken develops a deeper flavour when marinaded in the egg mixture, although if you don't have time, you can omit this step.