The CZTI (Cadmium Zinc Telluride Imager) onboard AstroSat is a high energy coded mask imager and spectrometer in the energy range of 20 - 100 keV. Above 100 keV, the dominance of Compton scattering cross-section in CZTI results in a significant number of 2-pixel Compton events and these have been successfully utilized for polarization analysis of Crab pulsar and nebula (and transients like Gamma-ray bursts) in 100 - 380 keV. These 2-pixel Compton events can also be used to extend the spectroscopic energy range of CZTI up to 380 keV for bright sources. However, unlike the spectroscopy in primary energy range, where simultaneous background measurement is available from masked pixels, Compton spectroscopy requires blank sky observation for background measurement. Background subtraction, in this case, is non-trivial because of the presence of both short-term and long-term temporal variations in the data, which depend on multiple factors like earth rotation and the effect of South Atlantic Anomaly (SAA) regions etc. We have developed a methodology of background selection and subtraction that takes into account for these effects. Here, we describe these background selection and subtraction techniques and validate them using spectroscopy of Crab in the extended energy range of 30 - 380 keV region, and compare the obtained spectral parameters with the INTEGRAL results. This new capability allows for the extension of the energy range of AstroSat spectroscopy and will also enable the simultaneous spectro-polarimetric study of other bright sources like Cygnus X-1.