Preheat oven to 450 degrees. Cook potatoes in salted boiling water until tender, 11 to 13 minutes. Drain. Return potatoes to pot, and shake over low heat to dry and fluff. Coat with oil, and season with salt.

Mix together 1 1/2 teaspoons salt and the cornstarch (this was new to me, and really made a huge difference in the flavor and crispness of the chicken!). Pat chicken dry with paper towels. Combine minced garlic and softened butter. Rub skin with butter, and season with salt mixture. Rub the inside of the cavity as well.

Place chicken, breast side up on sprayed baking sheet and tuck wings under. Tie legs together with kitchen twine. Scatter potatoes around chicken. Roast for 30 minutes. Remove from oven, and flip potatoes. Return to oven, rotating sheet. Roast until chicken juices run clear and an instant-read thermometer inserted into the thickest part of a thigh reaches 165 degrees, about 30 minutes more. Let chicken rest for 10 minutes before serving.