Remove the chicken from the fridge and allow to rest at room temperature for at least 30 minutes before cooking.
Mix 1/8 cup butter and miso paste together, and massage well under the skin of the chicken, even under the skin of the legs. Remove any clumps or excess paste to maintain a thin, even coating on the chicken. Rub the skin of the chicken with the remaining 1 tbsp of butter, and do not add any extra salt or pepper to the chicken.
Arrange the chicken and sweet potato on a roasting pan, and lightly drizzle some olive oil over the potatoes. Cooking the sweet potato for this long will give it a crispy outside and soft and fluffy inside, however if you would like them to be less browned, add the sweet potatoes to the roasting tray partway through the cooking. The sweetness of the sweet potatoes balances out the saltiness of the miso, and the juices in the pan will add an amazing flavour to the potatoes.
Cook the chicken in the oven at 425 F for about 1 hour and 30 minutes until it is golden brown. If you feel that the chicken is browning too quickly, particularly within the last 30 minutes of cooking, cover loosely with aluminum foil. The chicken is finished cooking when the juices run clear and when an instant read thermometer inserted into the breast reads 180 F, and the thigh reads 190 F.
When finished cooking, transfer the chicken to a cutting board and allow to rest for about 15 minutes before carving. Transfer the chicken to a platter after resting, and plate with the sweet potatoes.
Enjoy your beautiful chicken!