I harvest Wild fennel same as Basil, taking the leaves as I need them and cutting just above a joint. Can't say I have noticed them getting very much bushier though, but then I am growing on clay so they aren't that happy to start with
"The trouble with having an open mind, of course, is that people will insist on coming along and trying to put things in it." Sir Terry Pratchett
I think you would lose some flowers if you shorten the stems but this would be the time to do it and I can't think you would notice fewer flowers later. I feel like I'm constantly deadheading so you should be OK.
"The trouble with having an open mind, of course, is that people will insist on coming along and trying to put things in it." Sir Terry Pratchett
Posts