Kurdish, an Indo-European language spoken by over 30 million speakers, is considered a dialect continuum and known for its diversity in language varieties. Previous studies addressing language and speech technology for Kurdish handle it in a monolithic way as a macro-language, resulting in disparities for dialects and varieties for which there are few resources and tools available. In this paper, we take a step towards developing resources for language and speech technology for varieties of Central Kurdish, creating a corpus by transcribing movies and TV series as an alternative to fieldwork. Additionally, we report the performance of machine translation, automatic speech recognition, and language identification as downstream tasks evaluated on Central Kurdish varieties. Data and models are publicly available under an open license at https://github.com/sinaahmadi/CORDI.