The only thing I could so far identify as a true local dessert here is the mango sticky rice. A lot of Asian cultures traditionally did not use much sugar... if any at all. Desserts usually are fruits or sweet soups made of normally, for Western taste buds, salty ingredients.
The mango sticky rice falls into both categories. Fruit. Rice.
Recipe and photos available on this site. Caveat: I have not tried to make it following this particular recipe, so it is not an endorsement from me. They just have nice photos :) (caveat number two:
Mangoes are one of the main fruits of the area. However, mangoes are not always in season. Surprising, eh? And when not in season, they taste horrible. That's part of the reason mangoes have not been very widely received in the States. Imported, they often are picked before fully ripe. And a lot people don't know what a ripe mango tastes like, assuming what they ate is normal.
Here, during the offseason, the price for a mango get exponentially more expensive. And many restaurants refuse to serve the dessert, even if you bought and brought the mango yourself. Somethings, the Thais are not willing to see maligned. And mangoes and their mango dessert rice seem to fall in that category.