In recent years, a variety of interesting concepts have been proposed to enable the concealment of objects from detection or observation, including invisibility cloaking. For an object to remain truly transparent to an illumination wave, a cloak must restore the exact spatio-temporal profile of the wave, including both amplitude and phase variations across the entire illumination frequency spectrum, i.e., the full field. However, on the basis of their fundamental operating principles, present invisibility solutions force different frequency components of a broadband illumination wave to experience different phase variations, necessarily distorting the wave’s temporal profile and making the cloaking device inherently visible. In this work, we propose a new conceptual approach to the problem, enabling the realization of full-field broadband invisibility, experimentally demonstrated here for the first time to the best of our knowledge. This involves a customized and reversible redistribution of the illumination frequency content, allowing the wave to propagate through the object of interest while preventing any interaction between the wave and the object. We report the experimental concealment of a broadband optical filter from detection with a phase-coherent light pulse of 500 GHz bandwidth, showing full restoration of the complex temporal and spectral profiles of the pulse.