Chop the leek into three large pieces and place in a stockpot or large heavy-bottomed pan (don't turn on the heat yet).
Chop the carrot into large pieces and add to the pot.
Peel the onion and add to the pot. Add the thyme to the pot. Cut the garlic head in half, across the cloves, and add to the pot. Add the peppercorns.
Add the chicken carcass and wings to the pot. Pour in enough cold water to cover the chicken, about 2.8 litres/5 pints.
Turn the heat on to a gentle heat and bring the stock to a simmer. Simmer, covered, for 1½-2 hours.
After half an hour or so, remove any scum that rises to the surface with a ladle or a large spoon. Repeat as necessary.
At the end of the cooking time, strain the stock, discarding the vegetables and chicken pieces. Allow to cool. You can use the stock as it is, store in the fridge for up to three days, or freeze for up to three months for future use.