The mesoscopic organization of the human neocortex is of great interest for cognitive neuroscience. However, fMRI in humans typically maps the functional units of cognitive processing on a macroscopic level. With the advent of ultra-high field MRI (≥7T), it has become possible to acquire fMRI data with sub-millimetre resolution, enabling probing the laminar and columnar circuitry in humans. Currently, laminar BOLD responses are not directly observed but inferred via data analysis, due to coarse spatial resolution of fMRI (e.g. 0.7-0.8 mm isotropic) relative to the extent of histological laminae. In this study, we introduce a novel approach for mapping the cortical BOLD response at the spatial scale of cortical layers and columns at 7T (an unprecedented 0.1 mm, either in the laminar or columnar direction). We demonstrate experimentally and using simulations, the superiority of the novel approach compared to standard approaches for human laminar fMRI in terms of effective spatial resolution in either laminar or columnar direction. In addition, we provide evidence that the laminar BOLD signal profile is not homogeneous even over short patches of cortex. In summary, the proposed novel approach affords the ability to directly study the mesoscopic organization of the human cortex, thus, bridging the gap between human cognitive neuroscience and invasive animal studies.