Preheat oven to 450 degrees. Remove backbone from chicken. Flip chicken breast side up. Press firmly on the breastbone to flatten. Season both sides with salt and pepper.
Place chicken on a rimmed baking sheet. Toss together apple, fennel, leeks, and 2 tablespoons oil. Season with salt and pepper. Scatter around chicken. Cover chicken with prosciutto, overlapping slices and tucking edges underneath. Toss sage leaves with remaining 1 teaspoon oil and scatter on top. Roast until prosciutto is crisp, chicken is cooked through (an instant-read thermometer registers 165 degrees), and vegetables are tender and golden, 30 to 40 minutes. Loosely tent chicken with foil, and let rest 10 minutes before cutting into pieces.
All in One
Roast veggies alongside for a one-pan meal. Prosciutto draped over the bird means you get the salty ham in every bite.