To be honest, the fried chicken sandwich—the one people queue up for at noon on a weekday—was kind of an afterthought.

Chef Logan Cox had already poured his culinary ambitions into his full-service restaurant, Homer. (Our Restaurant of the Year last winter.) But he and his wife, Sara Knowles, thought it might be fun to open a bar down the street. A place where parents could sip negroni slushies while their kids smashed a soft serve swirl, sprinkled with graham cracker crumbles or bits of potato chip.

Knowles designed a cheerful white-wainscoted room that whispers of elegant soda fountains. The couple stocked some high chairs, named the place Milk Drunk, a soft serve and drinks joint that also pays tribute to their young daughter’s state of zoned-out bliss after feeding. (Three tipsy cheers for nursing-inspired cocktail bars.) Oh, and this place should probably have some food? The kitchen had space for two fryers, which seemed adequate for some chicken sandwiches and french fries.

“We learned the first day,” Cox recalls, “this was not the business venture we had planned.”

Bring me your finest mozzarella sticks.

Soft serve gets twisted (and topped).

The neighborhood lined up, six feet apart on the sidewalk, for chicken sandwiches. In that tiny kitchen, Cox and his crew battled hourlong waits and many days where all the 36 hour–brined chicken they could fit in their walk-in was gone by midafternoon.

His kitchen made some tweaks to accommodate the crowds. And while it wasn’t the original point of Milk Drunk, that chicken sandwich still benefits from the full spectrum of Cox’s talent: A thick thigh, brined then breaded in a ton of spices (garlic, coriander, even urfa biber) that connect this place to Homer’s broadly Mediterranean menu. The result isn’t spicy, but hums with flavor, like an engine under a hood. Cox devised five sandwiches (plus a veggie version with fried portobello). One benefits mightily from the whipped garlic that makes magic at Homer; spice seekers, get the chicken that’s topped with shaved country ham and hot honey.

Fried thighs aside, Milk Drunk works great as Cox originally intended, a destination for dessert and drinks. Though last year he probably wouldn’t have imagined he’d be dispensing such refined cocktails to-go, in two-person portions. Swirls of soft serve, in classic and seasonal flavors, get coated with hard shells (chocolate, caramel, or peanut butter) and your choice of toppings. The best part of the menu may be the one that’s received the least hype: Milk Drunk makes its own scratch mozzarella sticks. Imagine a food that’s already great as a shitty, industrial-grade bar food, then imagine it coated in the same spice medley as the chicken, then dredged in a rice panko that contains ranch powder.

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