We report on uniquely extensive new glacier thickness profiles covering 200 km of Himalayan glaciers in the Solu Khumbu basin around Everest. Glacier thickness maps are needed to determine the size of the world’s remaining mountain ice reserve and to model glacier dynamic response to melting, and projections of future mass loss are highly sensitive to the initial thickness distribution. Modelling of the global ice distribution involves largely unknown parameters that must be tuned with ice thickness measurements, but these are rare and skewed to the European Alps. In the Himalayan headwaters of the Brahmaputra, Indus and Ganges basins, home to 800 million people and 41,000 glaciers, the thickness of only 6 glaciers is reported, for example, with profiles covering only ~10 km. This data scarcity reflects the difficulties of surveying remote, high and sometimes debris-covered glaciers, which we overcame by using a purpose-built low-frequency helicopter radar. We describe this new survey, the challenges involved in extracting ice thickness from radar data, and the opportunities for systematic calibration of glacier thickness models throughout the Himalayas.