Many of the Greek restaurants that have opened on Long Island in the past 10 years offer a somewhat modern version of the cooking born from the kitchens of grandparents. Taverna 38 is noteworthy for executing these refined, traditional dishes at reasonable prices.

Owners Claudio Peralta and John Alexopoulos originally opened the modern Mediterranean Xarello in this space, but it didn’t catch on. Then, after six months, they changed the name and concept and Taverna 38 was born. Out went the old restaurant’s heavy red décor and in came a refreshing white dining room.

The kitchen here, which has been open since May, has already seen some changes. Panos “Peter” Tsaglis is the restaurant’s second executive chef, and he arrives from several Manhattan Greek restaurants with solid credentials. But there is one important constant in the kitchen, 71-year-old Dimitrios Alexopoulos, John’s father.

Dimitrios, born on the southwest coast of the Peloponnese region, makes the spanakopita. This no-nonsense hot appetizer has a shatteringly crisp phyllo dough crust filled with chopped and well-drained spinach, imported feta and has a clean dill taste. It’s that same straightforward approach with another appetizer, melitzanosalata. This roasted eggplant dip includes the same salty feta as the spanakopita and has a strong garlic flavor. While the accompanying grilled pita lacked personality, the creamy eggplant, roasted whole, skin-on then hand peeled and mashed, was bitterless and balanced enough to eat solo.

After the cold and hot appetizers and soups, the menu splits among seafood and meat-focused entrees along with five traditional dishes. No tricks on the moussaka; just long slices of fried eggplant and other vegetables between a layer of seasoned ground beef and creamy potatoes, topped with luscious béchamel.

The three grilled Colorado baby lamb chops (paidakia) were nearly perfectly cooked — though one was past rare — with meaty flavor. Marinated in Greek olive oil, garlic and herbs for a few hours before grilling, they arrive on a pile of Idaho potatoes roasted with oil and lemons.

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The seafood was less successful. An appetizer of mussels along with the shrimp in the seafood paella and the ones topping the pasta dish known as garidomakaronada were all tough. Better were the eight sautéed, tails-on shrimp served over a bed of orzo with mixed vegetables.

The crabcake (kabourokeftedes) was a fine example of how the dish should be assembled: two sizable patties that showcased lump crab, barely held together by panko-style bread crumbs pan fried to a crispy finish. Unfortunately, the same restraint wasn’t afforded to a massive portion of pastitsio. This baked ziti dish stuffed with ground lamb, beef, cheese and topped with béchamel was plated over a bed of rice and was heavy and overly rich.

While the dish isn’t his, Dimitrios also influences the flavorful olive oil cake, which has been on the menu since Xarello. The moist cake uses oil instead of butter for richness but is airier than most with a strong citrus taste enhanced by oil pressed from olives grown on Dimitrios’ land in Greece. A scoop of creamy frozen yogurt accompanies the cake, which is topped with strawberries and plump cranberries. Galaktoboureko, a semi-firm custard pie made with phyllo dough, had a creamy texture and arrived topped with honey.

Taverna 38 keeps prices reasonable without sacrificing quality or classic dishes such as whole fish (like branzino), or grilled octopus. The service is attentive, making it even easier to get comfortable in the narrow dining room.