Hi Rob. Good question. I had to dig into my copy of How to Make a Forest Garden, by Patrick Whitefield. He has a lot of good info on the subject of forest gardens. He names chicory as being a good dynamic accumulator which can be used for animal grazing or in a fertility patch. He says the wild plant is a perennial, but most chicories are treated as annuals because their taste becomes very bitter with age. He doesn't talk about chop and drop, but as it self sows, it might be possible to let babies grow and then chop the ones you don't want to eat. Cutting too much of plants you want might weaken the plant, but I don't know too much about this particular plant. You might want to pick out one or a few to go to seed to make more, and chop the rest.
I know with my sorrel plants, comfrey, and wild spinach, etc, I can cut quite a bit without seeming to hurt the plant--but eventually the leaves get smaller and the plant just looks sad.
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