  In this article we study a Standard Model extension modifying the top-quark
Yukawa coupling to the Higgs boson by allowing a mixture of CP-odd and -even
couplings. Single top-quark production in association with an additional Higgs
boson provides a natural laboratory to search for such extensions. However,
because of the small cross section the experimental analysis is challenging.
Already the measurement of the cross section for this process is highly
non-trivial. Furthermore, using only cross section measurements, a certain
parameter region would escape detection. Using an explicit BSM scenario we show
that employing the Matrix Element Method a precise measurement becomes
feasible. Ignoring signal detection efficiencies an integrated luminosity of
about 20 fb^-1 would allow a discovery. Assuming signal detection efficiencies
at the level of a few percent a potential signal could be established in the
high luminosity phase of the LHC.
