First let me state that Madame Queen is a difficult one for me so congratulations if you got it to a good size. It being such a fleshy rhizomatous, I would treat it like a succulent - let the cuts heal before sticking it in any moist media.

I cut a lot of rhizomatous this time of year due to the size they become in one summer. The warmer months would probably be better but if you have plenty of light and a warm place, you can grow it in winter as well. In fact you can do it by leaf cuttings as well.

I would not cut this back to the soil surface but play it conservative by leaving at least a few nodes so it can sprout there. If there is anything coming from the ground then you can cut the old rhizomes all the way back.

You can even take the small growths at the nodes off and start those as new plants (I did that for Freddie and glad I did since the old rhizomes seem to have given out).

Give the cuttings some extra humidity to encourage faster root growth. I often use the lettuce containers from the grocery stores to start rhizomes and leaves in. Shouldn't even have to water the soil if it is just a little moist.

Here is a small example of 3 Black Coffee rhizomes I cut back in March. I put those in 3 inch pots and placed all of them in a lettuce container and the lid over the top. They pushed the top off eventually and I removed it.

Perfect advice! That is the way to go hcmcdole. Follow those directions and off you go.