We develop a BiB3O6 (BiBO)-based optical parametric amplifier in the spectral region around 2 µm using a Yb:KGW amplifier operating at 100 kHz. The two-stage degenerate optical parametric amplification results in a typical output energy of 30 µJ after compression, spectrum covering 1.7-2.5 µm range, and a pulse duration fully compressible down to 16.4 fs, corresponding to 2.3 cycles. Due to the inline difference frequency generation of the seed pulses, the carrier envelope phase (CEP) is passively stabilized without feedback over 11 hours at the level below 100 mrad including a long-term drift. Short-term statistical analysis in the spectral domain further shows a behavior qualitatively different from that of parametric fluorescence, indicating high degree of suppression of optical parametric fluorescence. The high phase stability together with the few-cycle pulse duration is promising for the investigation of high-field phenomena such as subcycle spectroscopy in solids or high harmonics generation.