Method and system for the extraction of oils from a biomass with a liquid carbon dioxide using cosolvent. The system and method can be used to extract cannabinoids from Cannabis biomass by cryogenically freezing the biomass and exposing the Cannabis biomass to sub-cooled liquid carbon dioxide and capturing a first high-terpene extract fraction, and then exposing the Cannabis biomass with a mixture of superfluid carbon dioxide and a cosolvent to capture a high cannabinoid second fraction.