The path towards carbon-free aeronautical propulsion and power generation necessitates the adoption of new fuels. Among them, hydrogen offers a higher specific energy and its combustion in air produces no carbon compound. However, hydrogen flames raise two main issues: first, their high burning velocity promotes flashback, and secondly, NOx emissions are favored by the high adiabatic temperatures of these flames. To control these two phenomena, hydrogen and air must be quickly premixed to avoid hotspots, and the mixing has to be lean to reduce the flame temperature and NOx formation. From an industrial perspective, the flame has to be stabilized at a distance from the solid boundaries, which can be achieved using swirling flows. In this work, experiments are performed on a single-sector burner, already used to study premixed and spray hydrocarbon flames. The atomizer in the spray version of the burner is replaced by a new cross-flow injection system to produce pure hydrogen-air flames while taking into account those requirements. This injection scheme is investigated by exploring the domain of operation and analyzing the flame structures through light emission imaging and velocity measurements. Mixing under cold flow conditions is examined using laser tomography to determine the equivalence ratio distributions at the injector outlet. These systematic experiments help define operating conditions and design parameter ranges of interest.