Averievite, Cu$_5$V$_2$O$_{10}$(CsCl), is an oxide mineral composed of Cu$^{2+}$ kagome layers sandwiched by Cu$^{2+}$-V$^{5+}$ honeycomb layers. We have synthesized this oxide and investigated its properties from ab initio calculations along with susceptibility and specific heat measurements. The data indicate a Curie-Weiss temperature of 185 K as well as long-range magnetic order at 24 K due to the significant interlayer coupling from the honeycomb copper ions. This order is suppressed by substituting these coppers by isoelectronic zinc, suggesting that Zn-substituted averievite is a promising spin liquid candidate. A further proposed substitution that replaces V$^{5+}$ by Ti$^{4+}$ not only dopes the material, but is predicted to give rise to a two-dimensional electronic structure featuring Dirac crossings. As such, averievite is an attractive platform for S=1/2 kagome physics with the potential for realizing novel electronic states.