I don't like Vermouth in my martinis--just gin.
Will it work with good gin and just the feta brine plus olives?? While demonstrating making the Quinoa patties, you said "goat cheese". Are goat and feta interchaneable in this fritter.
Recipe question for: Feta-Brine Martini
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Nomenclature aside, just make it the way you like it. It's your bar, your taste buds.
If you like vermouth-less "martinis" made with other condiments, it is likely you won't miss the vermouth in this one. And if you want to call it a martini, that's fine. Pleasing you and your guests is the most important thing anyhow.