Adjust oven rack to center position and preheat oven to 500°F (260°C). Pat chicken dry with paper towels and season on all sides generously with salt and pepper. Line heavy-duty rimmed baking sheet with foil. Place chicken on foil, skin-side up. Transfer to oven and roast until thickest part of breast registers 150°F (66°C) on an instant-read thermometer, about 45 minutes (see note). Remove from oven, transfer chicken to a cutting board, and allow to rest for 15 minutes.
While chicken roasts, make jus. Chop neck and backbone into 1-inch chunks with a cleaver, heavy chef's knife, or poultry shears. Place in a medium saucepan and cook over high heat, stirring occasionally with a wooden spoon until browned on all sides, about 5 minutes. Add leek greens and bay leaves and cover with water. Simmer for 30 minutes, then strain, discarding solids. You should have about 2 cups of jus.
Place leek whites in a large saucepan and pour chicken jus on top. After chicken comes out of oven, bring leeks to simmer, reduce heat to low, cover, and allow to cook until leeks are tender and chicken is ready to serve, about 15 minutes. Season leeks and jus to taste with salt and pepper.
While chicken rests, place asparagus in the now-empty pan that the chicken was roasted in. Drizzle with olive oil and season with salt and pepper. Transfer to oven and roast until tender and browned, about 10 minutes.
Carve chicken into serving pieces. Transfer leeks to serving platter with a slotted spoon, leaving jus in pan. Stir butter into jus until emulsified. Transfer asparagus and chicken to serving platter and pour jus all around. Serve immediately.