Why broom?

Of course I have from my earliest childhood been familiar with the coat of arms of Guernsey. It consists of a shield with three lions, which is of course a familiar Anglo-Norman symbol, but with a more unfamiliar addition: a plant growing out of the top.

As a youngish schoolboy, I got curious about the plant. At some point I asked in the Priaulx library and was told that it was a sprig of broom. Slowly after that I began to realise that that raises more questions than it settles: what’s the significance of the broom? There is broom in the island, but nobody seemed to consider it iconic: if in the late 20th century anyone picked a plant to symbolise the island, it would much more likely have been gorse (“furze”).

At least twenty-five years later, my colleague Adam Fergus inadvertently made progress on this question for me, by giving me a copy of Bringhurst.

It states, in edition 4.3 (2019):

But Plantagenet is an old French name for the broom plant (in modern French, la plante genêt). It is said that Geoffrey of Anjou, founder of the family and an avid hunter, wore a sprig of it in his hat and had it planted as cover for birds.

That does at least start to explain why broom got into Anglo-Norman imagery, although it’s a bit short of suggesting a specific Guernsey connection. I wonder if there’s a fuller explanation.

I also note that the Wikipedia page for Guernsey’s coat of arms is very vague about it. The text mentions the sprig but doesn’t say what it is. The blazon given there (“Gules, 3 lions passant guardant Or, langued and armed Azure”) doesn’t mention the sprig at all.

Searching the web found also:

• A dedicated heraldry wiki page, which refers with evident disinterest only to a “small leaf”, clearly regarding the details as a distraction from its main purpose of being sniffy about how Guernsey, an entity autonomous from England, hasn’t been given permission from some organisation in England to use a symbol that it’s been using for more than seven hundred years (which is to say, two hundred years more than that organisation in England has existed).
• Another heraldry page with considerably more relevant information, which mentions broom in the arms of Guernsey (and of Alderney) explicitly.