Place chicken in a large pot and cover with cold water.
Bring slowly to a simmer over medium heat, skimming off any foam that rises to the top.
Add carrots, parsnip, leek, charred onion, bay leaves, and peppercorns.
Simmer gently, uncovered, for 1 hour 30 minutes to 2 hours, until the chicken is very tender.
Remove chicken, cool slightly, and shred the meat, discarding skin and bones.
Strain the broth, season with salt, and return the shredded chicken to the pot to warm through.
Ladle into bowls and top with fresh parsley.