We propose and theoretically demonstrate a novel type of optical Yagi-Uda nanoantennas tunable via variation of the free-carrier density of a semiconductor disk placed in a gap of a metallic dipole feeding element. Unlike its narrowband all-metal counterparts, this nanoantenna exhibits a broadband unidirectional emission and demonstrates a bistable response in a preferential direction of the far-field zone, which opens up unique possibilities for ultrafast control of subwavelength light not attainable with dipole or bowtie architectures.