ABSTRACT Cold ($\sim$10 K) and dense ($\sim 10^{5}$ cm$^{-3}$) cores of gas and dust within molecular clouds, known as starless and dynamically evolved pre-stellar cores, are the birthplaces of low-mass (M$\le$ few M$_\odot$) stars. As detections of interstellar complex organic molecules, or COMs, in starless cores has increased, abundance comparisons suggest that some COMs might be seeded early in the star formation process and inherited to later stages (i.e. protostellar discs and eventually comets). To date observations of COMs in starless cores have been limited, with most detections reported solely in the Taurus molecular cloud. It is therefore still a question whether different environments affect abundances. We have surveyed 35 starless and pre-stellar cores in the Perseus molecular cloud with the Arizona Radio Observatory (ARO) 12 m telescope detecting both methanol, CH$_3$OH, and acetaldehyde, CH$_3$CHO, in 100 per cent and 49 per cent of the sample, respectively. In the sub-sample of 15 cores where CH$_3$CHO was detected at $\gt 3\sigma$ ($\sim$18 mK) with the ARO 12 m, follow-up observations with the Yebes 40 m telescope were carried out. Detections of formic acid, t-HCOOH, ketene, H$_2$CCO, methyl cyanide, CH$_3$CN, vinyl cyanide, CH$_2$CHCN, methyl formate, HCOOCH$_3$, and dimethyl ether, CH$_3$OCH$_3$, are seen in at least 20 per cent of the cores. We discuss detection statistics, calculate column densities, and compare abundances across various stages of low-mass star formation. Our findings have more than doubled COM detection statistics in cold cores and show COMs are prevalent in the gas before star and planet formation in the Perseus molecular cloud.