Del Pedro, the managing partner of Tooker Alley, a bar in Brooklyn, pours an ounce and a half of tequila into a glass. He follows that with some genever, the malty Dutch gin. Then it really gets weird.

He adds a half-ounce of Parfait Amour, a liqueur tasting of vanilla and flowers that even the most curious of mixologists have opted to politely ignore.

He’s not done. Next comes a teaspoon of Martini bianco vermouth, with its strong note of oregano. Stirred over ice and strained into a coupe glass, the drink, which Mr. Pedro calls an Amethyst, is light lavender in color and tastes a bit like a violet candy.

It is not for everybody. Though the cocktail is ordered often, one out of every seven or eight is sent right back. And Mr. Pedro is fine with that.