We present optical coherence tomography (OCT) with 2 nm axial resolution using broadband soft X-ray radiation (SXR) from a compact laser plasma light source. The laser plasma was formed by the interaction of nanosecond laser pulses with a gaseous target in a double stream gas puff target approach. The source was optimized for efficient SXR emission from the krypton/helium gas puff target in the 2 to 5 nm spectral range, encompassing the entire "water-window" spectral range from 2.3 nm to 4.4 nm wavelength. The coherence parameters of the SXR radiation allowed for the OCT measurements of a bulk multilayer structure with 10 nm period and 40% bottom layer thickness to period ratio, with an axial resolution of about 2 nm and detect multilayer interfaces up to a depth of about 100 nm. The experimental data are in agreement with OCT simulations performed on ideal multilayer structure. In the paper, detailed information about the source, its optimization, the optical system, OCT measurements and the results are presented and discussed.