Preheat the oven to 425 degrees
Cut potatoes into 1" dice.
Place potatoes on 1/3 of prepared baking sheet and top with 2 tsp. olive oil and a pinch of salt and pepper. Massage oil and seasonings into potatoes. Spread into a single layer.
Roast in hot oven, 10 minutes.
Trim green beans, if necessary.
Coarsely crush crackers in a ziplock bag.
In a mixing bowl, combine crushed crackers, shredded cheese, and 1 tsp. olive oil. Set aside.
In another mixing bowl, combine half the Buffalo sauce (to taste; reserve remaining for garnish) and softened cream cheese. Set aside.
Pat chicken dry and season both sides with a pinch of salt and pepper.
After 10 minutes, carefully remove sheet from oven and flip the potatoes.
Place green beans in center of sheet and top with a pinch of salt, garlic pepper, and 2 tsp. olive oil.
Place chicken on empty side of sheet. Evenly top with Buffalo-cream cheese mixture (use less if spice-averse), then cracker-cheese mixture, pressing gently to adhere.
Roast in hot oven until potatoes are browned, green beans are tender, and chicken reaches a minimum internal temperature of 165 degrees, 15-20 minutes.
Carefully remove from oven. Top vegetables with softened butter and stir until melted and combined.
To serve, top chicken with remaining Buffalo sauce (to taste) and dressing!