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Asked about the many praises heaped upon his restaurant, Turkuaz Grill owner Mustafa Gulsen rattles off a handful of honorary designations the listicle-friendly restaurant has received over the years.

“Let’s see, there’s ‘hidden gem,’ ” he says, “[best] under the umbrella [dining], on the waterfront …”

The list goes on.

Of all the titles given to the Turkish restaurant over the years, though, there’s one that’s most special to the staff: a family business.

“I think people feel like they’re coming to visit our house when they come here,” said Deniz Gulsen, Mustafa’s wife and one of more than a half-dozen family members who help run the business. ‘They say, ‘I don’t feel like I’m at a restaurant, I feel like I’m in your home.’ ”

Turkuaz Grill’s journey to become one of Riverhead’s — and the North Fork’s — most admired restaurants was an unlikely one. Its roots are actually in a failed restaurant, Sultan’s Kitchen, which opened near the traffic circle on Route 58 in Riverhead in September 2001. In retrospect, Mustafa said, opening the community’s first Turkish restaurant — “with the word Sultan in the name” — within a month of the Sept. 11 terrorist attacks might have played a role in its demise. (He also acknowledges the location was a factor.)

David Benthal, editorial, portrait,

Mustafa grew up near Ankara, the capital city of Turkey, and came to America at age 15. The Westhampton Beach resident once managed a 7-Eleven and owned a deli in Flanders, but never lost a desire to bring the cuisine of his native country to his adopted hometown.

A second opportunity arose in 2009, when he took over the current site of Turkuaz Grill from a family member who’d been operating a more casual Mediterranean eatery at the location.

The Gulsens and the family members who help run the restaurant today — namely Deniz’s sister, Demet Bozatli, along with Ismail Ozturk and Kubila and Elvan Coskuntuncel — saw great potential in the small building at the eastern edge of the Peconic riverfront.

Deniz and Demet were born in Ankara, but later lived along the Aegean coast. The sisters saw a bit of home in this little slice of Riverhead.

Trained as graphic designers, the sisters incorporated those skills into the look of the restaurant, whose name translates to turquoise, a color that evokes the sea of their youths.

The transformation of the restaurant included touches as simple as upgrading from paper plates to ceramic and installing artwork that complements the restaurant’s more homey features, like a fireplace on the eastern wall of the dining room and dark wooden beams on its ceiling.

Outdoor dining is a big draw to Turkuaz Grill. (Credit: David Benthal)

The outdoor seating is a staple of the Mediterranean dining experience, the sisters say, and Turkuaz benefits from its position along the water.

“We see a lot of people enjoy their meal and then go for a walk along the riverfront,” Mustafa said.

The fact that the restaurant is located amid a string of downtown parking lots and does not face the main roadway could have been a curse, but it instead turned out to be a blessing. It’s hidden just enough to make patrons feel as if they’ve truly discovered something when eating there for the first time.

That dynamic has made Turkuaz a bit of a word-of-mouth sensation, something that was evident in the growth between its first and second summers in operation. That trend has continued, resulting in an expanse of repeat customers and steady flow of day-trippers.

“It’s a combination of word of mouth and technology,” Mustafa said of the restaurant’s growing popularity. “Social media has been big. People like and comment on Facebook and hundreds more people find out about us.”

Of course, none of this would matter if not for the quality of the food the family serves.

Demet said she and her sister “always said we wanted to have a business together where everything is from scratch.”

Branzino is a top dish at Turkuaz. (Credit: David Benthal)

Nothing the restaurant cooks with comes from a can, the sisters said. The hummus is made fresh throughout each day — and it would be challenging to find a better recipe elsewhere. They also use homegrown cucumber, dill and other ingredients in their cooking. Deniz said the generous use of olive oil is another secret to their western Turkey style of cooking.

As for the menu, the gyros and chicken kebabs are among the most popular dishes, Mustafa said, though he also encourages customers to try the grilled branzino.

Each of the relatives says working alongside family is something they embrace and, much like at home, no one plays any specific role.

“We’re waiters and waitresses, we’re cooks, we’re dishwashers,” Deniz said. “I think that’s something our customers see and respect.”

After a decade, they feel as if their own family has grown as returning patrons become an extension of it.

“Ten years later, we see our regulars with kids coming back with grandchildren,” Mustafa said.

“This place is filled with life,” Deniz adds. “It has come alive.”