Baijiu, a potent Chinese spirit with a notoriously hard-to-like taste, has been called everything from “liquid razorblades” to “the sweat of Satan.”

Now, the clear, powerful (up to 120 proof) sip that has a kind of licorice-meets-soy-sauce flavor even fans admit isn’t for everyone, is the new darling of the New York cocktail scene.

Though...