For the stock, using your hands, break the stripped chicken carcass into two or three pieces and place into a saucepan just large enough to hold them. (Alternatively, place the chicken bones into the pan.)
Add the remaining stock ingredients, pour over the water, then bring the mixture to the boil.
When the liquid is boiling, reduce the heat until the mixture is simmering, then continue to simmer, covered, for 40-45 minutes.
Strain the stock through a fine sieve and reserve the liquid. (About 800ml/1 pint 8¾fl oz of stock should be yielded. If not, add boiling water to the stock to make up the difference.)
Meanwhile, for the chicken with rice, heat the oil in a separate pan over a high heat. Add the onion and cumin seeds and fry, stirring well, for 1-2 minutes, or until the onions have softened and the cumin is fragrant.
Add the garlic, chilli, carrot and smoked paprika, stir well and continue to fry for 2-3 minutes, or until the carrots have softened.
Add the chopped tomatoes and pepper, then cook until the mixture is simmering gently. Cover the pan with a lid and cook for 8-10 minutes, or until the sauce has thickened.
Add the lager, stir well, then bring the mixture to the boil.
Add the chicken stock and return the mixture to the boil, then stir in the rice.
Reduce the heat until the mixture is simmering gently, then cover the pan and simmer for 25-30 minutes.
Turn the heat down to its lowest setting and continue to simmer for a further 8-10 minutes, or until the rice has absorbed all of the water and is tender.
Remove the rice from the heat, then stir in the peas, shredded chicken, chopped coriander and the juice of 1½ limes, (or to taste), until well combined. Season, to taste, with salt and freshly ground black pepper.
To serve, divide the arroz con pollo equally among four serving plates. Sprinkle over the remaining coriander. Garnish each plate with a lime wedge.