Zazas are generally considered to be part of the Kurdish ethno-cultural group and Zazai nationalism has been accused of being part of the Turkish attack on Kurdish nationalism in an attempt to separate the Zazas from the Kurdish movement. I don't know if or to what extent this is true.
Map of Iranian languages (Zaza(ki) in dark green in central Anatolia)
Grammatically Zazaki has some aspects in common with Kurmanji, such as genders (not found in Sorani or Persian) and the use of the ergative in the past tenses. However, it goes further than Kurmanji in that the verbs take gender agreement, compare for example:
bıray mın şı
brother-of me went
way mın şi
sister-of me went
So the verb 'went' changes to agree with the gender of the subject, here the feminine form is an ablaut of the masculine.
Now looking at a past tense, we can see that the verb agrees with the object due to the ergativity. The ergative basically means that the verb agrees with the object which takes the nominative case and the subject takes the oblique case so that it looks a little like a passive tense, but without any passive meaning. In English it would look something like: me has kicked the ball - here 'has' agrees with 'ball' even though the sentence means 'I kicked the ball'. The ergative is used in a few languages, Hindi/Urdu and Basque probably being the most prominent. In Zazaki, as in Kurmanji, the ergative is only applied to transitive verbs in the past tense, thus the examples above are not ergative since 'go' is intransitive.
So we can see:
mı dikê da to
me rooster gave you
I gave you the rooster
Here 'da' agrees with the masculine rooster which is the direct object of the action; the indirect object is simply placed after the verb. Compare this with:
mı kergê dê to
me hen gave you
I gave you the hen
Again here the verb 'dê' agrees with the object which is now feminine and again the verb changes through ablaut of the masculine form.
Here is an extract from the Little Prince in Zazaki, "Şazadeo Qıckek".
Ez ke şeş serri debiyan; rocê, yew kitabo be namey "Heykatê ke vêniyaê", gemê ke torzên cı nêkewtê, inan sero nusiyao, mi tede resmê do zaf rındek di bi. Resmê bi, sero marê boa heywanê dê yabani qult kerdêne. Kopya xo naya ita.
I can't gloss this text, but a few snippets aren't too difficult to figure out.
ez ke şeş serri debiyan
I when six year was-being
rocê, yew kitabo be namey...
one-day(OBL), a book with (the?)name
resmê do zaf rındek
picture ?? very nice-a
resmê bi, sero marê boa heywanê dê yabani qult kerdenê
picture was, in-which snake boa animal(OBL) gave? ??? swallow did?
As you can see, this barely shows us anything, but it gives you a chance to see what the language looks like and, to a very small extent, how it works. Unfortunately there is very little in the way of resources for Zazaki, although the causes for this are quite obvious considering the Turkish states dislike of minority languages.
Nevertheless, this is the language and culture of a couple of million people and so, despite the relative lack of information in this post, I don't think it is worthless since it is always worthwhile extending our knowledge a little on matters of such importance.
A Grammar of Zazaki/Dimli - http://www.zazaki.de/english/T.L.Todd-AGrammarofDimli.pdf
Paper on Zazaki by an old professor of mine - http://azargoshnasp.net/languages/zazaki/zazakipositionof.pdf
A good Wikipedia article - https://en.wikipedia.org/wiki/Zazaki_language