What are "cheese Parmentiers"? From Clarissa Dickson Wright's A History of English Food (2012):

[In the 1920s, British] hostesses also started to serve canapés: little cheese Parmentiers, asparagus rolled in thin brown bread and butter, delicate crab patties, and, of course, the ubiquitous vol-au-vents [...] (source)

Antoine-Augustin Parmentier (1737–1813) was a French proponent of the potato.
Googling &quot;cheese Parmentier&quot; just wants to tell me about hachis Parmentier, basically a French version of shepherd's pie, dating back to at least 1898. (&quot;Hachis&quot; here I think is French for &quot;a chopped-up thing,&quot; and has no relation to the Spanish word for &quot;hashish,&quot; but I'd appreciate some authoritative enlightenment on that point too.)
Hachis Parmentier does contain both cheese and potatoes, and also phonetically sounds like &quot;(ha-) cheese Parmentier&quot;; the only reasons I'm doubting this identification are (1) that I can't find any evidence at all that anyone's ever actually referred to hachis Parmentier as &quot;cheese Parmentier,&quot; and (2) little shepherd's pies sound like they'd make terribly messy canapés.
So, what did Clarissa Dickson Wright mean by &quot;little cheese Parmentiers&quot;?
Some quick Googling leads me to believe these are &quot;Bouchées Parmentier au Fromage&quot; (literally 'mouthfuls'), which seem to be some sort of potato-and-cheese croquette.
To find this, I did a Google image search for &quot;Parmentier au fromage&quot;. This shows many different dishes (lots of which are indeed shepherd's pie-like, but it also gives a few hits on the Bouchées. These seem to be perfect as a canapé, so fit the description in OP's question. Searching for &quot;Bouchées Parmentier au Fromage&quot; yields only these. It's admittedly not a water-tight argument, but it's the best I could find.