  We study asymptotically flat space-times in 3 dimensions for Einstein gravity
near future null infinity and show that the boundary is described by Carrollian
geometry. This is used to add sources to the BMS gauge corresponding to a
non-trivial boundary metric in the sense of Carrollian geometry. We then solve
the Einstein equations in a derivative expansion and derive a general set of
equations that take the form of Ward identities. Next, it is shown that there
is a well-posed variational problem at future null infinity without the need to
add any boundary term. By varying the on-shell action with respect to the
metric data of the boundary Carrollian geometry we are able to define a
boundary energy-momentum tensor at future null infinity. We show that its
diffeomorphism Ward identity is compatible with Einstein's equations. There is
another Ward identity that states that the energy flux vanishes. It is this
fact that is responsible for the enhancement of global symmetries to the full
BMS$_3$ algebra when we are dealing with constant boundary sources. Using a
notion of generalized conformal boundary Killing vector we can construct all
conserved BMS$_3$ currents from the boundary energy-momentum tensor.
