This paper proposes a new concept of designing compact high precision millimeter-wave wideband variable phase shifters. The phase shifter is implemented with a stacked shim with extremely short length of 0.9 mm and two waveguide flange adaptors with length of 0.5 mm. High precision phase shifting is achieved over entire D-band (110–170 GHz) by rotating the shim 90 degrees from aligned to perpendicular with consistent impedance matching performance. In addition, a glide-symmetric holey electromagnetic bandgap (EBG) structure is adopted to avoid wave leakage from the gap between the shim and the flange adaptors. A proof-of-concept (PoC) demonstrator is designed, manufactured, and tested. The measured results show that the designed stacked shim phase shifter with embedded EBG structure ensures return loss higher than 10 dB across 110–170 GHz with a 75 $\mu $ m airgap between waveguide flanges. The studied phase shifter provides a 0.88° phase shifting with each degree of mechanical rotation. The fabricated PoC phase shifter has a worst-case insertion loss of 0.92 dB and a return loss of 20 dB across the entire 110–170 GHz band and a maximum phase shift of 30°. At 10° phase shifting, the measured insertion loss is lower than 0.52 dB, and return loss is higher than 23 dB, respectively.