  Using the standard Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach, with
partial inclusion of next-to-leading order effects, we propose the inclusive
hadroproduction of a Higgs boson and of a jet, featuring large transverse
momenta and well separated in rapidity, as a new channel to probe the BFKL
dynamics. Predictions are presented for cross-sections and azimuthal angle
correlations in different kinematics configurations for the final-state
transverse momenta. We find that the large energy scales provided by the
emission of a Higgs boson stabilize the BFKL series.
