We were standing in my kitchen in Brooklyn, where Ms. Hirayama was about to show me the secrets of her rye tarte Tatin, once she coaxed Aly down from her arms with a bowl of sliced plums. Mr. Koreitem was already at the stove, blanching Tuscan kale leaves to blend into a sauce for pan-roasted cauliflower. Mia was at the table with a book.

After lunching at Mokonuts last summer, where I devoured white tuna crudo with chermoula and sorrel, and labneh cheesecake with nectarines and red currants, I asked the couple if they’d cook with me the next time they were in New York.

Blanching completed, Mr. Koreitem spooned the tender kale into the blender with toasted almonds and a nutty young pecorino cheese. He sampled the three olive oils in my pantry before deciding which to add. Then he squeezed in lemon, and puréed everything to a bright green pesto, tasting it constantly to adjust the oil, citrus and salt.

“I used to make this with Swiss chard,” he said, “but one day I couldn’t get it, so I tried cavolo nero, and it was just as good.”

Like many chefs of small Parisian restaurants, Mr. Koreitem changes the menu every day, responding to what he can get directly from his small group of farmer-purveyors. But, unlike many of his peers, he’s still apt to rework each dish, even when he can get the same ingredients two days in a row and sometimes in the middle of service, playing with new combinations of spices and condiments.

“I never stick with recipes,” he said as he seared cauliflower florets until charred on one side but barely golden on the other. “I like to cook by feel.”