We report on a simple scheme to generate broadband, μJ pulses centered at 2.1 μm with an intrinsic carrier-envelope phase (CEP) stability from the output of a Yb:YAG regenerative amplifier delivering 1-ps pulses with randomly varying CEP. To the best of our knowledge, the reported system has the highest optical-to-optical efficiency for converting 1-ps, 1 μm pulses to CEP stable, broadband, 2.1 μm pulses. The generated coherent light carries an energy of 5.4 μJ, at 5 kHz repetition rate, that can be scaled to higher energy or power by using a suitable front end, if required. The system is ideally suited for seeding broadband parametric amplifiers and multichannel synthesizers pumped by picosecond Yb-doped amplifiers, obviating the need for active timing synchronization. Alternatively, this scheme can be combined with high-power oscillators with tens of μJ energy to generate CEP stable, multioctave supercontinua, suitable for field-resolved and time-resolved spectroscopy.