We report on a nested-cavity, doubly resonant optical parametric oscillator (NesCOPO) architecture for widely tunable, mid-IR, single-frequency generation. By use of an achromatic phase-adapted double-pass pumping scheme, this new, low-threshold, semimonolithic architecture only requires two free-standing cavity mirrors and a nonlinear crystal with a mirror coating deposited on its input facet while the other facet is antireflection coated. It is thus as simple and compact as any basic linear optical parametric oscillator cavity, is easily tunable, and displays low sensitivity to mechanical vibrations. Using a high-repetition-rate (4.8 kHz) microlaser as the pump source of the NesCOPO, we demonstrate a compact source that provides pulsed, stable single-frequency output over a wide spectral range (3.8-4.3 μm) with a high peak power (up to 50 W), which are properties well suited for practical gas sensing applications.