I grew asparagus in my last garden...I just let the fern grow until it died off...it's quite pretty whilst waiting for the delicious spears.

Yes the "Fern" is a modified inflorescence that virtually all Asparagus species use for photosynthesis instead of true leaves that are reduced to scales or thorns in some species. Once the roots have become established after a couple of seasons, these emerging "ferns" can be cut before they expand and eaten.

Have you ever considered growing it from seed? There are some really good strains out now that will be croppable in two seasons and you will have loads of plants. I think Thompson & Morgan do one that a former work colleague grew after I told him about it. He was amazed at how quickly they reached cropping size.