  The study of the Higgs boson's properties is a cornerstone of the LHC and
future collider programs. In this paper, we examine the potential to directly
probe the Higgs-top interaction strength and CP-structure in the $t\bar t h$
channel with the Higgs boson decaying to bottom-quark pairs and top-quarks in
the di-leptonic mode. We adopt the BDRS algorithm to tag the boosted Higgs and
exploit the $M_2$-assisted reconstruction to compute observables sensitive to
the CP-phase at the $t\bar{t}$ rest frame, where the new physics sensitivity
can be enhanced. Performing a side-band analysis at the LHC to control the
continuum $t\bar{t}b\bar{b}$ background, we find that the Higgs-top strength
and CP-phase can be probed up to $\delta\kappa_t\lesssim 20\%$ and $| \alpha |
\lesssim 36^\circ$ at 95% CL, respectively. We also derive that a similar
analysis at a 100 TeV future collider could further improve the precision to
$\delta\kappa_t\lesssim 1\%$ and $| \alpha| \lesssim 1.5^\circ$, where the
CP-odd observables play a crucial role, boosting the sensitivity on the
CP-phase.
