Preheat your oven to 425°F (220°C). Line a large baking sheet with parchment paper.
Place the 1 ½ pounds baby gold potatoes and 1 pound green beans directly onto the baking sheet. Drizzle the vegetables with 2 tablespoons olive oil and season with 1 teaspoon salt and 1 teaspoon black pepper. Toss everything directly on the pan and spread into an even layer.
Arrange the 6 chicken thighs on top of the vegetables, skin side up.
In a medium bowl, whisk together 4 tablespoons melted unsalted butter, 5 cloves minced garlic, ½ cup grated parmesan cheese, ⅓ cup mayonnaise, 1 teaspoon Italian seasoning, ½ teaspoon paprika, and 1 tablespoon lemon juice.
Spoon the parmesan garlic sauce evenly over the chicken thighs.
Bake for 40 to 45 minutes, until the chicken reaches an internal temperature of 175°F (80°C), the potatoes are tender, and the chicken skin is golden.
Let the sheet pan rest for a few minutes before serving.