  The coupling between electrons and phonons is one of the fundamental
interactions in solids, underpinning a wide range of phenomena such as
resistivity, heat conductivity, and superconductivity. However, direct
measurements of this coupling for individual phonon modes remains a significant
challenge. In this work, we introduce a novel technique for mapping phonon
dispersions and electron phonon coupling (EPC) in van der Waals materials. By
generalizing the quantum twisting microscope to cryogenic temperatures, we
demonstrate its capability to map not only electronic dispersions via elastic
momentum-conserving tunnelling, but also phononic dispersions through inelastic
momentum-conserving tunnelling. Crucially, the inelastic tunnelling strength
provides a direct and quantitative measure of the momentum and mode resolved
EPC. We use this technique to measure the phonon spectrum and EPC of twisted
bilayer graphene (TBG). Surprisingly, we find that unlike standard acoustic
phonons, whose coupling to electrons diminishes as their momentum goes to zero,
TBG exhibits a low energy mode whose coupling increases with decreasing twist
angle. We show that this unusual coupling arises from the modulation of the
inter-layer tunnelling by a layer-antisymmetric 'phason' mode of the moir\'e
system. The technique demonstrated here opens the way for probing a large
variety of other neutral collective modes that couple to electronic tunnelling,
including plasmons, magnons and spinons in quantum materials.
