People don't usually refer to these scented, flower-shaped treats as "shortbread cookies" in Thailand. What I mean is that if you visit Bangkok and go around asking people to direct you to a place where they sell "Thai shortbread cookies," you'll most likely get a bunch of knitted brows, tilted heads, rapid blinks, and complete silence.
However, ask for Khanom Kleeb Lamduan (official Romanization: Khanom Klip Lamduan) and mental light bulbs turn on instantly. If there's any problem, it would be that they don't know which snack shop to send you to for the best. There are just so many of them all over the city.
Shortbread cookies? Yes. You may not agree, but I do believe that stripped of its external appearance, scent, and all the cultural connotations attached to it, that's essentially what Kleeb Lamduan is. They're not different at all from what's generally regarded as shortbread cookies in the West: tender-crumbed, sandy, melt-in-your-mouth cookies. They're even made in a similar manner.
The recipes for these cookies vary (ditto with recipes for shortbread cookies), but not by much, and they are all very simple. The recipe I use is one of the simplest ones I've seen and also one of the easiest to remember: two parts flour, one part powdered sugar, a bit of salt, and just enough oil or, as was done in my household when growing up, rendered leaf lard to get the dough to come together.
I've been using this same recipe since I was a kid learning how to bake. It has never failed me. The only tweak I've made over the years is to switch from all-purpose flour to cake flour as I've found that even though all-purpose flour works just fine, flour with lower protein content seems to work better in creating the desired texture.
Now let's address the shape issue. And, yes, it is more important than it seems. Why? You see, and I have no clue who invented these cookies and what went through the inventor's mind, the cookies are traditionally fashioned after a fragrant flower, lamduan (Melodorum fruticosum Lour.), which is native to Southeast Asia.
Hence the name. To shape these cookies any other way and call them by the same name will create the kind of disconnect that will make the Thai people grab their temples in confusion.
This means that even though nobody can, or should, force you to shape the dough in tiny flower-shaped cookies—which takes so much time and dexterity—you may want to consider doing it anyway. Fine. I'll beg. Please do it.
For one thing, without this unique appearance, these cookies are completely indistinguishable from any old shortbread cookies. Also, shaped this way, the cookies have more surface area than if they were to be shaped into coins like typical sablé cookies. The semi-crisp edges of the petals, and I hope I'm not imagining this, make the cookies more tactilely pleasant.
The only remaining issue to address is the scent. Traditionally, Kleeb Lamduan cookies are perfumed with Tian Op, Thai scented candle. So these cookies end up smelling pretty much the same regardless of what shop you buy them from. Now that I think about it, I have never come across any Kleeb Lamduans that don't carry the scent of Thai dessert candle (they would have stood out like a sore thumb in my memory).
Tian Op can be found at some very well-stocked Asian grocery stores, but you'll probably have better luck finding them online. They're not expensive, can be reused several times, and last a long time. They're also fun to use. Plus, they make it possible for you to say outrageous things, like, "Oh, I'm not doing anything - just sitting around smoking cookies. You?"