Preheat oven to 425F. Place potatoes, onions and carrots into the dutch oven and toss with 1 tbsp olive oil. Season with 1 tsp salt and ¼ tsp pepper. Toss to coat evenly.
Unwrap chicken and remove anything from the cavity. Pat dry with a paper towel. Use a basting brush to spread melted butter under the chicken skin on the breasts, thighs and legs.
Brush 1 tbsp of olive oil over the top of the chicken skin. Season with salt and pepper. Place chicken in the dutch oven on top of the veggies, breast side facing up. Place lid on the dutch oven
Bake at 425F for 1 hour with the lid on. Remove the lid and cook uncovered for another 10-30 minutes depending on the weight of the chicken. Remove from the oven when the internal temperature of the chicken thigh is 165F
If you want extra crispy skin, broil the chicken for just 1-2 minutes before removing from the oven.
Remove the chicken from the dutch oven and allow to cool for about 20 minutes before carving and serving with the roasted vegetables. Drizzle excess juices from the dutch oven over the sliced chicken.