  After the discovery of the 125 GeV scalar boson with gauge properties similar
to the Standard Model Higgs, the search for beyond the SM interactions will
focus on studying the discovered particles' coupling properties more precisely
and shedding light on the relation of fermion masses with the electroweak
vacuum. The large mass of the top quark and the SM-predicted order one top
Yukawa coupling is a natural candidate for BSM physics, though experimentally
challenging to constrain. In this paper, we argue that investigating angular
correlations in $pp\to tHj$ production provides an excellent handle to
constrain the top Yukawa coupling $y_t$ via direct measurements, even when we
focus on rare exclusive final states. We perform a hadron-level analysis and
show that we may expect to constrain $y_t\gtrsim 0.5\, y_t^{\text{SM}}$ at
95%-99% confidence level at the high luminosity LHC using semi-leptonic top
decays and $H\to \gamma \gamma$ alone, by employing a two-channel measurement
approach.
