At the age of 16, Allen Katz tried to debone a rabbit in his family’s kitchen in Baltimore. He wanted to make rabbit pâté for Thanksgiving, though he had no idea what it should taste like.

“I don’t think I did a very good job,” said Katz, now 44, a mixologist and founder of New York Distilling Co. in Brooklyn.

But he found that he liked the tenacity the experiment demanded. It fit with his family’s traditions: celebrating every major holiday with “two days of cooking, two days of eating,” he recalled, and adding suspense to Thanksgiving with an elaborate turkey alternative (venison, duck, rockfish-stuffed crab) unveiled at the last minute.

This idea — that time spent cooking can be as gratifying, even as romantic, as time spent eating — may explain Katz’s commitment to his Oxo food mill. (Technically, it belongs to his wife, Samantha; he gave it to her for Hanukkah six years ago.) “I want to sweat a little bit in the kitchen, then sit down, listen and laugh,” he said.

The food mill comes with feet, for resting atop a bowl, and three grades of stainless-steel sieves of increasingly fine perforations. These may be switched out to achieve varying degrees of velvetiness in soups and sauces — as well as “every manner of purée,” Katz said, the primary mission when his daughter, Elsie, was born. Now 2 1/2 years old, Elsie can twirl the handle herself.

Still, the tool “requires patience,” Katz said. He first used a mill around the time he encountered the phrase “slow food,” while teaching at a culinary school in Italy. (The Slow Food movement grew out of a 1986 protest against the opening of a McDonald’s by the Spanish Steps in Rome.) Back home — “in a fit of melancholy; why did I leave?” he said — he called Slow Food USA to volunteer. He wound up chairman of its board.

At home in New York City, Katz simmers cinchona bark, berries and petals, then runs the slurry through the mill to make tonic, as a partner for his company’s gins. His approach to mixing cocktails, like cooking, is part theme and variations, a legacy of his musical childhood (Suzuki violin, clarinet, piano, guitar), and part historical research. He intends to taste every drink from “The Bon Vivant’s Companion,” the first compendium of American cocktail recipes, originally published in 1862 by Jerry Thomas, the Noah Webster of bartenders.

New York Distilling specializes in gin and rye whiskey, which Katz considers the most important spirits from the 19th century’s golden age of cocktails. “That died off with Prohibition,” he said. “Only now have we reclaimed our taste buds. There don’t have to be just benign flavors that deliver alcohol.”

The company’s most recent release, Ragtime Rye, took six years to produce. Grain was planted in upstate New York in 2009 and distilled in 2012; the first bottles went on sale this month.

“It’s important to us to say, ‘We made it,'” Katz said. “To politely, purposefully do things differently.”