In this work, we propose an Automated Speech Recognition Differential Testing Framework (ASDF) for testing Automated Speech Recognition (ASR) systems. ASDF is an extension of CrossASR++, an existing ASR testing tool that automates the audio test case generation process. However, CrossASR++ does not make efficient use of the input corpus and does not provide useful information on the failed test cases for ASR improvement. To resolve this, ASDF fills in the gaps by implementing differential testing into CrossASR++ through various text transformation methods. ASDF provides a targeted and controlled increase in audio test case generation by applying text transformation methods to the original text inputs that failed during the ASR testing process, therefore effectively creating new high-quality test cases for ASR systems from the existing text corpus. ASDF eliminates the need for a large number of audio test cases to be sourced or generated for testing ASR systems, which is a weakness found in CrossASR++. In addition, ASDF records useful information for ASR analysis by using various metrics. ASDF also performs phonetic analysis on the failed test cases which identifies and graphs the phonemes that ASR systems tend to transcribe incorrectly, providing useful information for ASR developers and researchers in the future. Video demonstration: url{https://www.youtube.com/watch?v=DzVwfc3h9As}.