This is a braise, of course, and so a warming and winterish meal — but it is brighter tasting than your usual pot roasts and stews, and so lends itself perfectly to this mildening of weather, this subtle shift from snow to sleet. Your kids don't need to be great adventurers to like soy-braised chicken, which is also sometimes called "red-cooked chicken": it is tender and burnished, with that addictive soy-sauciness, which they will love, and then some unusual but pleasant seasonings including cinnamon, orange, and ginger.
I suggest skinless bone-in chicken thighs in this dish, because they are so inexpensive and delicious and the long, salty cooking seems somehow to rid them of the various ropynesses and sinewish what-all that can scare me. But you could use any skinless, bone-in parts you like: I used to have the butcher cut up a whole chicken into 10 pieces, and that was also a wonderful way to prepare this recipe. The beauty here is that you don't even have to brown anything: it all goes right into the pot and simmers away for a couple of hours, unattended. Truly easy.
The only two things you could have any trouble finding are the star anise and the Szechuan peppercorns--and you know what? If you can't find them, leave them out. It will still be delicious. But if you've got a Whole Foods or an Asian market nearby, pick up a tiny bit of each.
Serve with brown rice and orange slices.
While you deal with the chicken (skinning it, e.g.), bring the rest of the ingredients to a simmer in a large pot over high heat.
Turn the heat down and add the chicken, then cover the pot and cook at a mild simmer for up to 2 hours
Serve the chicken with some of its sauce spooned over the rice.