Date cookies are thin and spread out
Presumably, you're following a standard cookie recipe that creams together butter and sugar, mixes with some flour, and adds leavening and other stuff. 

In my experience, thin cookies are usually the result of two things: too much liquid, and white sugar. The ratio of dry ingredients to wet ones should be pretty self explanatory: for thicker cookies you might want to try adding less liquid, and/or more flour.

More likely is that you're using too much white sugar. White sugar liquifies at a high enough temperature, and in cookies this translates to a spreading out of the dough while baking. Then when the cookies are cooled and the sugar crystallizes again, the cookies become hard.

To remedy this, start by substituting half of the white sugar in your recipe for brown sugar. You can also try experimenting with other sweeteners such as molasses and honey, which should also help the cookies stay thicker (and likewise more cakey). Just keep adjusting the ratio of white sugar to other sweeteners until you get the texture you like.