A visit to Eulalie begins, inevitably, with an outgoing voice-mail message. That alone may be disqualifying for whole swaths of would-be diners; Eulalie is on no reservation apps and has no official website. “You have found us in the wonderful and historic Tribeca,” announces the voice of Tina Vaughn, who, with her husband, Chip Smith, runs Eulalie in the address recently vacated by Bâtard. This is not a short message. It comes with news (it is fully booked), rules (“We do so appreciate your best in terms of attire … think more Mad Men and less Grubhub”), and an invitation to leave a message and be called back because, as Vaughn says, “we are so looking forward to welcoming you.”

She means it, too. “Welcome to the house!” Vaughn crowed on a recent Tuesday. Eulalie takes its name from a vineyard in the south of France, named by its winemaker for his wife, though it also calls to mind Edgar Allen Poe’s matrimonial poem, about a man who “dwelt alone / In a world of moan / Till the fair and gentle Eulalie became my blushing bride.” After the Klimtian moodiness of Bâtard the space has been stripped to a kind of Colonial plainness with pea-green, mostly unadorned walls and yards of white tablecloth. But Vaughn warms her dining room like a roost, and the whole place has a family feeling. I had been only once before, but already I had a usual table.

The couple arrived in Tribeca by way of the Upper East Side, where they ran the Simone for nearly a decade in a townhouse on East 82nd Street. Uptown, they were already an anachronism, but in Tribeca, next door to Frenchette, they seem like time travelers. They have imported stately peculiarities such as the pen-and-ink reservation book and menus swoopily handwritten by Vaughn. Her hair is a little more silvered than it once was; Smith’s is now crew-cut short. But the food is as it was uptown: fancy in a way that is no longer fashionable, like the menu’s constant soufflé. “This is like what they’d serve at the White House,” one of my dining companions said wonderingly. Eulalie may be, by design, the least cool
restaurant in New York.

Smith’s menu — currently served as a $115 prix fixe — is a tour through a Silver Palate–ish sophistication. Every dinner starts with terrine for the table (the variety of which is rotated every two weeks), with brioche toasts and homemade pickles, and a midcourse quenelle bobbing in a little bowl of oceanic sea-bass soupe de poisson and crowned with caviar. Among the starters, you might bow to the overriding ambience and have a savory mushroom tart, a square of homemade puff pastry atop a zigzag squiggle of balsamic reduction, or the soufflé of the moment — goat cheese one visit, blue cheese another. But — and I am aware that I am striking at the heart here, so I -apologize — the soufflés were puckish and dense on both my visits. If you see trotter among the appetizers, crisp and golden on the outside but crumbling at a touch to gamy tenderness, get that instead. It comes with turnips and a “pot likker” of their greens, a nod to the owners’ southern heritage. (Their first restaurant was in Kitty Hawk.) “This is the best foot I have ever eaten,” a tablemate remarked.

On my visits, I didn’t have an entrée that approached that peak, though I enjoyed an agreeable roasted chicken breast with a foie-larded ballotine of thigh and a musky little plug of veal loin. Desserts too were standard fare: crème brûlée, chocolate pot de crème, a dense slice of cherry cake.

Eulalie is not the best restaurant in the city, but at the moment, it is among the finest. To be fussed over and flirted with and reminisced-to about long-ago trips through Provençal wine country as rosé splashes, unrequested, into your glass, is to enter a softer world, amber-preserved. You are invited, encouraged, to linger at the island of your table, a humane and comfortable distance from any neighbors. Some tables even sit empty to maintain the peace. “‘Full’ for me is a sexy 42,” Vaughn says. “We prefer to keep it quiet and under the radar.”

According to the Upper East Siders I canvassed, some of the Simone’s old neighbors found the critical appreciation mystifying; one declared the place positively geriatric. But every under-40 I took to Eulalie — not one of whom had heard of it — was in rapture. “This is what a restaurant should be,” said an “It” girl I know, who swanned past my table. The city groans with perfect food; much rarer is perfect hospitality. Take it from a professional eater. I supped alone in a world of moan…