Preheat oven to 400°F (200°C). Line a large sheet pan with parchment paper or foil for easy cleanup.
Prepare the seasoning:
In a small bowl, mix olive oil, melted butter, garlic, paprika, thyme, rosemary, oregano, salt, pepper, and red pepper flakes.
Season the potatoes and carrots:
Toss potatoes and carrots with half of the seasoning mixture. Spread them on the sheet pan in a single layer.
Add the chicken:
Place the chicken thighs (or breasts) skin-side up on the sheet pan. Brush with the remaining seasoning mixture.
Roast for 25 minutes.
Add the green beans:
Toss green beans with a drizzle of olive oil and a pinch of salt and pepper. Add them to the sheet pan around the chicken and potatoes.
Roast for another 15-20 minutes, until the chicken is golden and reaches an internal temperature of 165°F (75°C).
Finish & Serve: