Heat oil in a large saucepan on low. Add onion and carrot and cook for 7 minutes, until beginning to soften. Add thyme and peppercorns and cover with 6 cups water. Increase heat to medium and simmer for 10 minutes. Add chicken, cover and simmer for 10 minutes. Remove pan from heat and set aside for 15 minutes.
Remove chicken from stock with a slotted spoon and set aside. Strain broth into a clean saucepan and discard flavourings. Heat broth on low until simmering. Add garlic and celery and simmer for 5 minutes, until soft.
Shred chicken and add to broth with celery leaves and bread. Simmer for another minute to heat through. Season well and serve.