Anyone who has ever had prolonged contact with Japanese food will recognize the basis of these "cookies" -- mochi is used in many places in Japanese cuisine, including being used as a wrapper for ice cream. Daifuku is plain, sweet mochi wrapped around red bean paste, another Japanese favorite. Many people find it grows on them.
The microwave mochi is from http://www.kitchenlink.com/msgbrd/board_0/2001/JAN/54508.html .
2 cups mochiko flour
1 to 1½ cups sugar
2 ¼ C water
corn- or tapioca starch
Azuki (red bean) paste, preferably smooth
Mix ingredients well until lump-free -- it will be thin. I spoon it into a set of microwaveable cupcake molds, as it is easy to just scoop individual servings of mochi out with a spoon; the original recipe suggests a large lightly greased microwaveable tube or ring cake container.
Microwave on high for 7 minutes (12 minutes for the tube container). Scoop out with a spoon or slice into cubes and roll in corn- or tapioca starch. The consistency before the starch is much like handling a ball of tacky rubber cement; the starch makes it much easier to handle.
Let the mochi cool until just warm. One at a time, flatten the mochi ball to about ¼" thick and place a small dab (¼ to ½ tsp) of bean paste in the center. Bring the edges together and pinch to fasten them -- this takes practice, so don't be discouraged if you don't get it right away. Seal in the bean paste by pinching the mochi shut, and go on to the next ball. Makes about 8 daifuku.