Look at the seed pods/heads/fruits forming on these weeds. If the seeds are not yet mature, still soft and pale, you can safely compost/mulch. If these seeds are mature enough to be viable, you can compost IF you can get the pile extremely hot -- the way to do this is compost this stuff on its own, mixed with a bit more "green" matter (grass clippings would be good), some "brown" matter (straw or chopped leaves, and add a potent N source -- a bit of lawn fertilizer or similar. Keep it moist, turn it, and let it cook so it gets really hot. That will kill any seeds. Alternatively, bag and dispose of. But, the high temp composting does work if done right.

I'm the only person that I know of to experience a sting; it was totally my fault...I stepped on her with my bare foot. ==>> ya know.. stepping on something.. and crushing the life out of it.. and then blaming it for stinging you.. is.. well .. a unique explanation.. lol perhaps physics might suggest.. that you self-inserted the stinger into your foot .. lol i have had one hovering over the deck for two days now.. i had forgot what they were.. so thx OP for reminding me.. but i have to tell you.. i waive my hand.. and it skedaddles ... but i have to say.. i havent tried waving my nor rhiz's foot at it.. so who knows if it might self insert its stinger into me ... gotta go find something useful to do.. besides pull rhiz's leg .. or foot.. plagues come and go over the years.. their population is dependent on the kady pop ... if you had a big kady population last year.. that is probably why you have many of these this year.. but they may decimate the population of kadys [if you dont kill them all]... so kady go down.. and eventually they go down.. etc ... its a viciouls predatory cycle.. solving itself.. if you dont interfere too much ... as far as i am concerned.. individuals.. ignore them ... i dont know what to tell you if there are a lot ...most likely.. their active phase is short lived.. basically. they dig a hole.. lay an egg.. go get a kady.. stuff it in the hole.. close it up and leave ... abandoning that hole and the child [whats that all about].. i dont know how many times they do it .. i though only once.. but it may have been one egg per hole ... you might want to look into their life cycle .. and perhaps.. in fall if the eggs remains so for that long.. a simple turning of the soil.. will disturb the multiyear cycle you are worrying about knowledge is power.. lets defeat these suckers ... but lets try to avoid.. going nuclear on them.. if you can deal with it ... i would give them the space.. and consider them a free show of my garden.. but then.. i have 5 acres.. and giving them a section.. wouldnt bother me ... good luck ken

How big of a garden spot is this? It looks like it would be easier and much quicker to pull up the "good plants" and smother the whole spot for a year. Then uncover a small test spot & check to make sure it's well & truly dead before putting it back into use. Smothering won't work if not done thoroughly, heavy corrugated cardboard with seams overlapping at least 6", no holes in it, covered with at least 4" of heavy organic matter holding it down and completely blocking the light, and for sure covering all of the plant/roots. I think I would use 2 layers of it for this plant, one I couldn't kill when I tried getting rid of the top 6" of soil in a garden about 20 yrs ago. I've never had smothering not kill anything but this particular plant gives me the heebie jeebies. Good luck with whatever you attempt!

Meconopsis cambrica. I love them and use them a lot in my garden. They tolerate shade, have no pests that I've ever come across and require no care whatsoever. They self sow but I just remove the ones in places where I don't want them. They are biennial. Here it is with another self sower, Geranium maderense.