Lay out the chicken, spreading out the parts as much as possible. Cover generously with 3 tablespoons of the fennel spice, rubbing it into the skin. Place a large pot over medium-high heat. When the pan is hot, add 6 tablespoons of the oil and heat to almost smoking. Add the chicken and brown on all sides, about 5 to 6 minutes per side. Add the celery, carrot, onion and bay leaves and sauté for a few minutes. Add 4 cups of water to the pot, or enough to cover the chicken. Bring to a gentle simmer and cook just until the chicken is almost fully cooked, about 40 minutes. Turn off the heat and cover and let cool. When pan has cooled, place in the fridge overnight.
Lift out the cooled chicken and strain the stock, discarding the solids. Refrigerate or freeze the chicken stock for another use.
Remove the skin and bones from the chicken. Shred the meat by hand into rough bite-size pieces.
In a large bowl, combine the shredded chicken, celery heart, red onion, 6 tablespoons olive oil, 2 tablespoons lemon juice, remaining 1 1/2 teaspoons Fennel Spice Rub, and salt and pepper, to taste. Add more oil, lemon juice, or Fennel Spice Rub, if desired. Add the basil and serve.
Fennel Spice Rub:
Yield: about 1 1/4 cups
Put the fennel seeds, coriander seeds, and peppercorns in a heavy pan over medium heat. Watch carefully, tossing frequently so the seeds toast evenly. When light brown and fragrant, pour the seeds onto a plate to cool. They must be cool before grinding, or they will gum up the blades.
Pour the seeds into a blender and add the salt. Blend to a fine powder, shaking the blender occasionally to redistribute the seeds. Store in a tightly sealed glass jar in a cool, dry place, or freeze.