The breast meat of chicken cooks much more rapidly than does the leg meat. When overcooked, it - like any foodstuff consisting of protein - dries and toughens. Keeping it tender presents a bigger challenge when you cook it in liquid than when you roast it, because the liquid is a more efficient cooking medium than oven heat.
This is the first flaw, it seems to me, of poule-au-pot recipes, which instruct you to boil the bird whole. The second is that they also tell you to cook your vegetables to the pot, adding them at intervals, according to how long you think they need. The chances are that some will emerge overcooked.
1 chicken, or hen (poule)
1/2 chicken stock cube
2 bay leaves
Joint the chicken, or get the butcher to do it for you. I cut mine into eight pieces: I separated the thighs and the drumsticks, and cut the breasts in half.
Put the thighs, drumsticks, backbone and giblets (if you have them - but minus the liver) into the bottom of a stockpot or deep casserole. Pour in water just to cover, and bring to a simmer. Skim the froth (though it is harmless - chefs get rid of it in order to avoid producing murky stock). Throw in the half stock cube, onions, bay leaves, and peppercorns. Cover (for thoughts on covering stock, see here), and simmer for 60 minutes. (I, liking very tender leg meat, allowed 90 minutes.) Add the breast portions. There is no need to turn up the heat to bring the liquid back to a simmer - it is hot enough. Cover, and allow another 30 minutes.
Chop off the tough leaves of the leeks, cut them down the middle, and slice. Soak them in water, to get rid of the grit. Transfer them (without their soaking water) to a saucepan, pour over a serving spoonful of stock from the chicken pot, add a knob of butter and some salt, cover and cook on a low to medium heat for five minutes. Uncover the pan and continue to cook, stirring, until the liquid has evaporated.
Peel the carrots and cut them into thick batons. Cook them in the same way as the leeks, but allowing them 10 to 12 minutes in the covered pan before removing the lid and evaporating the liquid.
We had our chicken with rice as well. Plain, boiled potatoes (new or maincrop) would also have been fine.
Serve the chicken with a spoonful or two of its stock. Keep the rest of the stock to use in other recipes. A salsa verde, or a garlic mayonnaise, would be a good accompaniment.