Antennas capable of providing high gains while occupying minimal volume can facilitate several technologies, such as 5G, CubeSats, and automotive radars. This work designs, analyzes, and measures a low-profile, metal-only offset stepped parabolic reflector antenna. The reflector aperture consists of a discrete number of parabolic sections that reflect the incident electromagnetic fields with a modulo 2π phase shift resulting in a collimated far-field beam. The technique can efficiently result in profile heights of the order of one wavelength, making it very desirable for mmWave applications. The reflector can be fabricated using computer numerical control (CNC) machining and 3-D printing. As a representative prototype, an offset stepped reflector with an aperture diameter of 20 cm, an F/D of 0.5, and a profile height of 0.79 cm at 19 GHz is analyzed, built, and measured. The periodicity of the surface results in a high sidelobe envelope, which is analyzed, numerically modeled, and verified through measurements. Guidelines on how to remedy the high sidelobe envelope are provided, and the associated tradeoffs are highlighted. Furthermore, the stepped reflector geometry introduces a scan in the main beam as the frequency deviates from the center frequency. This phenomenon is also verified through measurements and explained through analytical formulations.