Chop the carrot and celery into 5cm/2inch pieces. Peel and quarter the onion.
Add all the ingredients to a large pot.
Cover with water.
Bring to the boil then immediately reduce to your hob's lowest heat. Simmer for 2 hours, occasionally discarding any froth that may collect on the top.
Using a large slotted spoon, remove all the vegetables and as much chicken, bones and skin as possible.
Place a fine mesh bag over a jug and pour the remaining liquid into it. Strain out all the liquid.
Allow to cool and transfer to an air tight container. Store in the fridge.
Notes
If you want to make sure that you are extracting as many nutrients from the chicken bones as possible, then add a little splash of apple cider vinegar to the stock. You won't be able to taste it.
Try not to break or crush the carcass in the pan, as this will discolour the stock and you want a nice clear stock.
If the stock produces any foam when cooking, skim that off to give a clearer stock.
As the stock cools in the fridge, the fat will rise to the top and solidify. You can scrape this off if you want a clearer stock for using in chicken noodle soup. But if you are using it to make a flavour packed stew, there is no need to do this.
You need to use a pan big enough for everything to fit snuggly in. Don't worry if the bones stick out a little at first, as they will collapse as they cook.
If you want this stock to go further, then add a stock cube and 250ml extra water. You will still have that homemade flavour, but it will stretch a big further.
Season your stock as you go and add more as needed.