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Abstract We investigate the inclusive hadroproduction of a heavy quarkonium ( $$J/\psi $$ J / ψ or $$\Upsilon $$ Υ ), in association with a light-flavored jet, as a testing ground for the semi-hard regime of QCD. Our theoretical setup is the hybrid high-energy and collinear factorization, where the standard collinear approach is supplemented by the t-channel resummation of leading and next-to-leading energy logarithms à la BFKL. We present predictions for rapidity and azimuthal-angle differential distributions, hunting for stabilizing effects of the high-energy series under higher-order corrections. Our reaction represents an additional channel to test the production mechanisms of quarkonia at high energies and large transverse momenta and to possibly shed light on the transition region from heavy-quark pair production to single-parton fragmentation of $$J/\psi $$ J / ψ and $$\Upsilon $$ Υ states.