  Shadow tomography aims to build a classical description of a quantum state
from a sequence of simple random measurements. Physical observables are then
reconstructed from the resulting classical shadow. Shadow protocols which use
single-body random measurements are simple to implement and capture few-body
observables efficiently, but do not apply to systems with fundamental number
conservation laws, such as ultracold atoms. We address this shortcoming by
proposing and analyzing a new local shadow protocol adapted to such systems.
The "All-Pairs" protocol requires one layer of two-body gates and only
$\textrm{poly}(V)$ samples to reconstruct arbitrary few body observables.
Moreover, by exploiting the permutation symmetry of the protocol, we derive a
linear time post-processing algorithm. We provide a proof-of-principle
reference implementation and demonstrate the reconstruction of 2- and 4-point
functions in a paired Luttinger liquid of hardcore bosons.
