My basic thinking is that I would make cookies flavored with rose water and fill them with homemade jam. I already had a couple jars of raspberry jam that I had made a little while back. So, I then racked my brain as to how to incorporate the lychees. I couldn't find a recipe for lychee jam anywhere, and with such a watery fruit, I was reticent to improvise. My concern is that the chopped lychees would leech out most of their liquid in the cooking process, resulting in a syrup with a few bits of fruit floating on top. Jelly was also an option, but I couldn't find a recipe and again, the expense was daunting. So, I decided to just forget the lychees for now and instead use some homemade apple jelly that I had on hand. I combined half raspberry jam and half apple jelly for my filling. If you can't do without lychees, I'd just mince some fresh or canned ones and add those to raspberry jam.
Onto the cookies themselves. I wanted thin, crisp, lacy cookies. I took cues from Alton Brown for achieving this and used baking soda in lieu of baking powder, milk in place of one egg, and a high proportion of white sugar to brown sugar. For those interested, I used his recipe for "the thin", but omitted the chocolate chips, replaced the vanilla extract with a tablespoons of rose water, and added a few drops of rose food coloring.
This turned the batter a pretty pink color, but only a slight tint was visible in the finished cookies. If you want more of a pink color, you might substitute butter-flavored shortening for the butter (or extra-virgin coconut oil plus a bit of imitation butter flavoring, or clarified butter). The cookies won't be as crisp, but due to the lack of milk solids they ought to brown less and thus the pink color will be more prominent. By the way, my cookies were baked in half the time suggested by the recipe, so check them often.
Here's the finished product. 1/3 cup of apple jelly + 1/3 cup of raspberry jam should be sufficient for the whole recipe. Just slather a thin layer of of the filling on the bottom side of one cookie, then top with another, bottom side facing the jam. The result is a precious little tea cookie with wonderful flavor. It's no Ispahan, but it's an admirable substitute if you can't get the real thing!