We present a 2-μm all-fiber laser in which a highly chirped fiber Bragg grating (CFBG) sets the net cavity dispersion to −100.9 ps2. Within an energy-managed laser architecture, this large anomalous dispersion enables the mode-locking of energetic and narrow-band pulses featuring: 17.8 nJ energy, 15.2 ps duration, and 0.36 nm bandwidth. These results validate that mode-locked laser oscillators incorporating CFBGs can generate picosecond pulses in the 2-μm wavelength region and demonstrate that, when combined with energy management, simultaneous scaling of pulse duration and energy is achieved. Experimental observations are well reproduced by numerical simulations.