Step 1: Preheat your oven to 425°F (220°C). Remove the chicken from its packaging, remove any giblets from the cavity, and pat it thoroughly dry with paper towels.
Step 2: Place the chicken in a roasting pan. Drizzle with olive oil, then rub it all over, including under the skin if desired. Season generously with salt and black pepper.
Step 3: Roast the chicken for 15-20 minutes at 425°F (220°C), then reduce the oven temperature to 375°F (190°C) and continue roasting for another 60-75 minutes, or until a meat thermometer inserted into the thickest part of the thigh (avoiding the bone) reads 165°F (74°C).
Step 4: While the chicken roasts, place the peeled and quartered potatoes in a large pot and cover with cold water. Add a pinch of salt. Bring to a boil, then reduce heat and simmer until the potatoes are fork-tender, about 15-20 minutes.
Step 5: Drain the potatoes thoroughly and return them to the hot pot. Add the softened butter and warm milk. Mash until smooth and creamy. Taste and adjust seasoning with additional salt and pepper as needed.
Step 6: Once the chicken is cooked, remove it from the oven and transfer it to a cutting board. Tent loosely with foil and let it rest for 10-15 minutes before carving. Serve immediately with the creamy mashed potatoes.