  In this paper we investigate the extension of high energy resummation at LLx
accuracy to jet observables. In particular, we present the high energy resummed
expression of the transverse momentum distribution of the outgoing parton in
the general partonic process $g(q) + g(q) \to g(q) + X$. In order to reach this
result, several new ideas are introduced and exploited. First we prove that LLx
resummation is achieved by dressing with hard radiation an off-shell gluon
initiated LO process even if its on-shell limit is vanishing or trivial. Then
we present a gauge-invariant framework where these calculations can be
performed by using the modern helicity techniques. Finally, we show a possible
way to restore gluon indistinguishability in the final state, which is
otherwise lost in the resummation procedure, at all orders in $\alpha_s$ at
LLx. All partonic channels are then resummed and cross-checked against
fixed-order calculations up to $\mathcal{O}(\alpha_s^3)$
