A mild copper mediated borylation protocol of alkynyl cyclic carbonates has been developed. Depending on the nature of the borylating reaction partner, either stereoselective diborylation of the propargylic surrogate takes place providing convenient access to (E)‐1,2‐borylated 1,3‐dienes, or traceless mono‐borylation that leads to α‐hydroxyallenes as the principal product. The dichotomy in this borylation protocol has been scrutinized by several control experiments illustrating that a relatively small change in the diboron(4) reagent allows for competitive alcohol‐assisted protodemetalation to forge an α‐hydroxyallene product under ambient conditions.