Preheat the oven to gas 5, 190°C, and fan 170°C. Warm the olive oil on the hob over medium-high heat in a casserole or ovenproof pan large enough to hold the chicken comfortably. Add the chicken breast-side down and sear until the skin is golden.
Turn the chicken, so it is sitting breast-side up, then reduce the heat to medium-low and add the leeks and celery. Cook for 3 minutes, then add the parsnips, stock, and 500ml (17fl oz) of water. Bring to the boil, then cover with a tightly fitting lid. Transfer to the oven and cook for 1 hour.
Remove from the oven and stir in the lentils. Put the lid back on and return to the oven for 15 minutes. Remove from the oven and skim most of the fat from the surface of the broth; discard. Stir in the spinach and peas, then season to taste. Set aside for 5 minutes.
Transfer the chicken from the casserole to a board, letting the liquid drain away from the cavity. Carve the meat into portions and return to the casserole dish to keep warm.
To make the pistou, put the garlic, spinach, basil, olive oil, and 2 tbsp water in a mini food processor. Whizz until finely chopped, then season to taste. (Use immediately, or cover and chill for up to 3 days.)
To serve, portion the chicken, veg, and broth in shallow bowls and top with a dollop of pistou and sides.
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