Summary: Exceptional food and good service.
Wife and I had a special dinner here over Labor Day Weekend. The half-rotisserie-chicken (a special?) was PHENOMENAL. We've never had such flavorful, juicy, tender chicken before. Imagine a Costco rotisserie chicken, but with more flavor, less fat, higher quality meat, and a much more skilled chef cooking it. The Pellegrino Pappardelle was excellent, though I had it with the "zuchini spaghetti" option. Definitely get it with pappardelle if your diet allows (mine did not), because that's a better combo than the zuchini. However, the zuchini was perfectly spiraled/cooked, so do not hesitate if you can't do gluten :)
French onion soup was excellent.
Exotic mushroom and brie stuffed inside a puff-pastry was as divine as it sounds. The mixed greens was a little too bitter for my wife I think, and she wished the dressing was more citrusy to cut through the fatty goodness of the brie. I'd recommend an appropriate white wine pairing, should you order this.
The caramel vanilla ice cream (home made!) was excellent.
Staff and service were excellent. They knew the menu and made solid suggestions.
The only dish I did not enjoy was the brussel sprouts. Their outside was a little too charred for my liking, though the inside was tender. The sauce was... not my favorite, but it was OK. Halloumi isn't my favorite cheese in general, but some bits were also grilled more than I'd like.
I think the chef and his wife run this lovely restaurant. If/when we return to the Hamptons, I'm going to ask that we get a reservation at Ete and work our schedule around that. Easily 5 stars.