Melt a tablespoon of butter with a tablespoon of olive oil in a large pot then add the onion, leek, celery, broccoli stalks and garlic. Season with salt and pepper.
Sauté until soft, fragrant and starting to brown then add the stock/broth, chicken breasts and bay leaves. Cover and allow to simmer gently until the chicken is cooked. Remove the chicken from the soup and shred with two forks. In the meantime, cook the gnocchi in a large pot of salted water.
Add the shredded chicken back to the soup with the cooked gnocchi, broccoli florets and cream. Allow to simmer until broccoli is cooked then season with salt, pepper and lemon juice before serving.