The significance of the olive oil is mirrored in the name of the hotel. The ideal number of days it needs to snow every year to produce the perfect olive oil on Dugi Otok is said to be 3.3. Meanwhile, “Nai” means “snow” in Old Dalmatic, an extinct language from the region. Hence Villa Nai 3.3.
On one morning of my trip, I get to take in the oil and natural splendour of Villa Nai 3.3 at several different locations, as part of a group tour.
At every stop, like caricatures of seasoned wine connoisseurs, we are encouraged to sniff the bouquet of each olive oil before swilling it around our mouths and savouring its rich, heady flavour.
We start the tasting at the hotel’s private pier, jutting out into the sparkling turquoise waters of the Zadar archipelago in northern Dalmatia, before moving on to a peak overlooking the property.
From there, we are able to observe how brilliantly designed Villa Nai 3.3 is. The famous Croatian architect, Nikola Bašić, has ensured that the one-storey hotel – built entirely from bright, locally excavated limestone – blends seamlessly into the landscape.
The olive oil is used all over the hotel, from the pâté massage and the delicious olive oil tea welcome drink to the hotel’s signature cocktail, The Olivetto.
Shaken by its creator, the barman William, as though he is auditioning for a remake of the Tom Cruise film Cocktail, it mixes olive oil with gin, egg white and Korlat, a local liqueur combining honey with herbs. This olive oil-infused drink slips down very nicely indeed.
Olive oil plays an equally prominent role in the hotel’s high-class cuisine. Everything from the local speciality “soparnik”, an 80cm-wide Croatian version of a Cornish pasty stuffed to the gills with chard, fennel and garlic, to a red mullet caught just hours before and cooked on a hanging griddle over an open fire at the Grotta outdoor restaurant, is immeasurably improved by lashings of olive oil.
Even if you’re not as keen on olive oil as Popeye is, there is still loads to do on this island, such as taking a boat trip around the gorgeous Kornati National Park and exploring some of the 140 uninhabited islands that are scattered around it.
Leaving the tiny port of Zman on Dugi Otok, I am immediately treated to a very special moment when our boat is joined by a frolicking pod of dolphins who playfully indulge in some formation dancing with our boat. Are they auditioning for a potential new TV show, Strictly Come Dolphins?
Later, we stop on another island, Kornat, at the remote Saint Mary’s Church, which was constructed in the Byzantine era. The key to the church is kept in a slot by the entrance so that storm-tossed fishermen can always find shelter there during turbulent weather.
On another day, we scale the 164 steps to the top of the 42-metre-high Veli Rat lighthouse on the north-western tip of Dugi Otok. The tallest lighthouse in the Adriatic Sea, it was built in 1849 and plastered with more than 100,000 egg yolks, which produce a highly resilient coating. Fortunately, the lighthouse smells of sea salt rather than way-past-its-best omelette.
The climb is a serious workout, but it’s worth it for the view from the summit. On a clear day, you can see all the way to Italy, 60km away.
Villa Nai 3.3 has it all, then. It is the perfect get-away-from-it-all destination. The eight rooms are ingeniously designed to be completely private, and judges from the Leading Hotels of the World group (to which it belongs) have deemed it the cleanest hotel in the world.
Down the centuries, everyone from Julius Caesar and Benito Mussolini to George Bernard Shaw and European Champions’ League-winning footballer Luka Modrić has fallen in love with this most enticing part of Croatia. It’s very easy to see why.
You have ravishing seas, gorgeous scenery and beautiful, historic sites.
Oh yes, and the world’s finest olive oil.
Red Savannah (redsavannah.com) offers a five night stay at Villa Nai 3.3 from £3,225 per person based on two adults sharing a deluxe sea view room on a bed and breakfast basis, with private return transfers from Split and return economy flights from London Luton to Split with EasyJet.