I've seen 22-inch beauty dishes used with Canon speedlights for portraits. However I'm not sure if a single speedlight is powerful enough for a large beauty dish. Should I be using it with a monolight strobe instead?
It depends entirely on the guide number of your flash, the distance to your subject, the brightness of your environment, whether you're using just a single or multiple flashes and I'm sure lots of other things.
I have seen large beauty dishes used without problem but it depends on your own circumstances.
A beauty dish is mainly used to focus back the light of a strobe It's basically like putting a flash 5cm away from the face of your subject, but without having the real flash in the photo It gives you that nice fallof of the light
It can only focus one light to one location to make one subject look good. If it's bigger, it will allow you to focus your light further away from your flash, but you shouldn't need more power, because in theory you need the same amount of focused light on your subject's face, and none is lost. In practice though, we're not using perfect mirrors, and some light will be lost.
And if it's close, well, you don't need a crazy powerful strobe