When should I cut the mustard?

With the possible exception one plant that has a seed like an over-sized grass burr, I appreciate ALL the plants that volunteer to help me in greening my part of the desert. (Or is it I who is attempting to help them?) One in particular I am wondering about is a plant in the mustard family called London Rocket (Sisymbrium Irio). I'd like to maximize it's ability to contribute to building the soil as well as allow the seeds to spread so it is well seeded for future years. Currently, except for shaded areas, the plants have turned brown and dropped most of their leaves making a nice mulch covering for the otherwise mostly bare soil. I'm thinking it should be left standing until at least the seeds are mature and dispersing. Is there any benefit to cutting the plant after that time or is it just as well to leave it standing? Would it have been more beneficial to do some pruning earlier in the year when the plant was lush green? I'm thinking that may have worked to cause some root die-off and then regrowth of both roots and the foliage.

I've been doing something similar for about 3 years now, neighbors think I'm too lazy to do the "weeding" lol. The way I see it, if I can let the London rocket reseed and drop mulch for me, it's one less chore, plus the bugs get some shade, Meanwhile the roots did my tilling, and when the plant dries up those root passages make the next plants roots go further and further down, all without me having to lift a finger. The most I do is machete the stems low to the ground around this time of year. Fukouka style seeding works well with this method. I am very interested in the work you are doing.