We report a high-gain, cw-pumped regenerative amplifier which is based on Ho-doped crystals and seeded by a versatile broadband source emitting between 2050 and 2100 nm. The regenerative amplifier is implemented in a chirped-pulse amplification system operating at room temperature. Using Ho:YLF as gain medium, 1.1 mJ pulses with a 50 ps pulse duration and a 10 kHz repetition rate are generated at 2050 and 2060 nm, corresponding to an average power of 11 W. Using the same seed source, a 10 kHz Ho:YAG regenerative amplifier at 2090 nm is studied in the same configuration. In all cases the regenerative amplifier parameters are chosen to operate in a tunable single-energy regime without instabilities.