Peroxygenases are heme‐dependent enzymes that use peroxide‐borne oxygen to catalyze a wide range of oxyfunctionalization reactions. Herein, we report the engineering of an unusual cofactor‐independent peroxygenase based on a promiscuous tautomerase that accepts different hydroperoxides (t‐BuOOH and H2O2) to accomplish enantiocomplementary epoxidations of various α,β‐unsaturated aldehydes (citral and substituted cinnamaldehydes), providing access to both enantiomers of the corresponding α,β‐epoxy‐aldehydes. High conversions (up to 98 %), high enantioselectivity (up to 98 % ee), and good product yields (50–80 %) were achieved. The reactions likely proceed via a reactive enzyme‐bound iminium ion intermediate, allowing tweaking of the enzyme's activity and selectivity by protein engineering. Our results underscore the potential of catalytic promiscuity for the engineering of new cofactor‐independent oxidative enzymes.