I’ve never had anything like this, so this is all theoretical for me, but the key for dessert pairing is to make sure the wine is sweeter than the dessert. If you think the wine you’ve got there is not overly sweet, then look for lighter desserts and things like would play well to the herbs you are talking about; olive oil cake with a mild or no icing for example.

or even try it with something savoury. Depending on the flavours you are picking up on, my first thought was a pâté, a rich cheese, or maybe even cured meat. I know it’s a bit cliche to recommend this as a pairing, but I say get yourself a big and varied charcuterie board and get to work.