Preheat the oven to 425°F. Line a sheet pan with parchment paper or spray it with cooking oil.

In a medium bowl, combine the potatoes with 1 to 2 minced garlic cloves, 2 tablespoons olive oil, 2 tablespoons grated Parmesan, and salt and pepper. Toss until evenly coated.

Spread the potatoes in a single layer on one third of the sheet pan. Roast for 10 to 15 minutes to give them a head start.

In the same medium bowl, mix 2 tablespoons olive oil, 2 minced garlic cloves, 1/3 cup grated Parmesan, 1/3 cup breadcrumbs, 1/2 teaspoon cracked black pepper, and 1/2 to 3/4 teaspoon sea salt.

Press this mixture onto each chicken breast to coat thoroughly.

Remove the pan from the oven and arrange the coated chicken breasts beside the partially roasted potatoes. Leave space for hot air to circulate.

Toss the green beans in the bowl with 1 tablespoon olive oil, 1 minced garlic clove, 1 tablespoon Parmesan if using, and salt and pepper. Add them to the sheet pan.

Return the pan to the oven and bake for about 25 minutes, or until the chicken's internal temperature reaches 165°F and the potatoes are fork tender.

For an extra crispy crust and browned potatoes, switch the oven to broil on high for 4 to 5 minutes, watching closely to prevent burning.

Remove the pan and let everything rest for several minutes before serving.