Preheat oven to 425°.
Remove and discard giblets and neck from chicken; trim excess fat and discard. Starting at neck cavity, loosen skin from breasts and drumsticks by inserting fingers, gently pushing between skin and meat.
Liberally salt and pepper the chicken. Stuff the cavity with half of the rosemary, lemon slices and 2 tsp. garlic.
Combine Butter, 1/2 of the rosemary, lemon juice, 1/2 teaspoon salt, 1/4 teaspoon pepper, and garlic in a small bowl. Rub seasoning mixture under loosened skin and over breasts and drumsticks.
Tie ends of legs together with twine. Lift wing tips up and over back, and tuck under chicken. Place chicken, breast side up, on a rack coated with cooking spray, and place rack in a roasting pan.
Sprinkle again with salt and pepper
Toss potatoes (or Brussels sprouts), carrots and onion with the remaining 1 tablespoon oil and salt and pepper. Arrange vegetable mixture evenly around chicken.
Bake at 425° for 1 1/2 hours or when juices run clear or until a thermometer inserted in meaty part of thigh registers 170°.
Remove chicken from pan; let stand 15 minutes. Sprinkle the potatoes with remaining 1/4 teaspoon salt and 1/4 teaspoon pepper.
Remove skin from chicken; discard. Carve chicken, and serve with potatoes and additional lemon wedges.
Note: Using a rack pan is optional. Having the chicken raised off the vegetables will help make the back side of the chicken a bit crispier and the juices from the chicken will make your veggies have a more carmel color.