Context. Methanol and complex organic molecules have been found in cold starless cores, where a standard warm-up scenario would not work because of the absence of heat sources. A recent chemical model attributed the presence of methanol and large organics to the efficient chemical desorption and a class of neutral-neutral reactions that proceed fast at low temperatures in the gas phase. Aims. The model calls for a high abundance of methanol ice at the edge of the CO freeze-out zone in cold cloud cores. Methods. We performed medium-resolution spectroscopy toward three field stars behind the starless core L 1544 at 3 μm to constrain the methanol ice abundance and compare it with the model predictions. Results. One of the field stars shows a m...