Combine 1 1/2 tablespoons garlic, 1/2 teaspoon salt, 1/2 teaspoon pepper, and sage in a small bowl. Remove and discard giblets and neck from chicken. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Lift wing tips up and over back; tuck under chicken. Rub garlic mixture under loosened skin. Place chicken, breast side up, on rack of a broiler pan coated with cooking spray. Place rack in broiler pan.
Combine potatoes, squash, butter, 1 1/2 teaspoons garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Arrange vegetable mixture around chicken. Bake at 400° for 1 hour or until a thermometer inserted into meaty part of thigh registers 165°. Let stand 10 minutes. Discard skin.
Wine note: For an affordable wine to pair with this dish, pick a dry riesling from Washington state, like Chateau Ste. Michelle's 2007 (Columbia Valley; $9). It has peach and orange flavors that create a tempting aromatic package with the sweet flavors of Roast Chicken with Potatoes and Butternut Squash. —Sara Schneider