Host cells that are engineered to produce benzylisoquinoline alkaloid (BIAs) precursors, such as norcoclaurine (NC) and norlaudanosoline (NL), are provided. The host cells may have one or more engineered modifications selected from: a feedback inhibition alleviating mutation in a enzyme gene; a transcriptional modulation modification of a biosynthetic enzyme gene; an inactivating mutation in an enzyme; and a heterologous coding sequence. Also provided are methods of producing a BIA of interest or a precursor thereof using the host cells and compositions, e.g., kits, systems etc., that find use in methods of the invention.