The difference with your standard is you can't cut back to the ground (called coppicing) and keep the shape, or even the same plant if it is grafted. So the furthest back you can go is to stubs coming from the knob which all the branches originate, called the knuckle. This type of pruning is called pollarding, and has been done on willows for centuries, with the harvested twigs used for things like fuel (firewood). Pollarding is basically coppicing high enough that your livestock can't eat your new shoots in the spring, leaving you with plenty of meat and no way to cook it.
Not sure which willow you have, but if they're anything like other common willows I suspect you could cut it back like that fairly often - perhaps even every year if you want. If I did it often I would trim it back to the knuckle when dormant (no leaves) - that way you know the tree has stored the maximum amount of energy it can to fuel regrow the next year. Make sure, if you do so, that you leave a little stub - don't try and go flush with the trunk. Unlike regular pruning, where you don't want a branch in that spot, with pollarding/coppicing you DO want another branch to grow there, so you need to leave enough stub to save a bud from which that new growth can originate.
This is a good project for that really nice, warm, sunny day that comes in early March where you want to get out and do something but don't want to dig in or crawl around on the wet soil. That also allows you to enjoy the colorful bark all winter if you variety has that trait. In fact, that bark (and colorful variegated leaves) are often a trait born only (or at least more dramatically) by young wood, so these days coppicing and pollarding are more often done to encourage those aesthetic traits, rather than for the harvested branches. Well, unless you're on Janet's zoo crew - then it is for both.