  We develop an effective field theory (EFT) framework to perform an analytic
calculation for energy correlator observables computed on groomed heavy-quark
jets. A soft-drop grooming algorithm is applied to a jet initiated by a massive
quark to minimize soft contamination effects such as pile-up and multi-parton
interactions. We specifically consider the two-particle energy correlator as an
initial application of this EFT framework to compute heavy quark jet
substructure. We find that there are different regimes for the event shapes,
depending on the size of the measured correlator observable, that require the
use of different EFT formulations, in which the quark mass and grooming
parameters may be relevant or not. We use the EFT to resum large logarithms in
the energy correlator observable in terms of the momentum of a reconstructed
heavy hadron to NLL$'$ accuracy and subsequently match it to a full QCD
$\mathcal{O}(\alpha_s)$ cross section, which we also compute. We compare our
predictions to simulations in PYTHIA for $e^+e^-$ collisions. We find a good
agreement with partonic simulations, as well as hadronic ones with an
appropriate shape function used to describe nonperturbative effects and the
heavy quark hadron decay turned off. We also predict the scaling behavior for
the leading nonperturbative power correction due to hadronization.
Consequently, we can give a prediction for the energy correlator distribution
at the level of the reconstructed heavy hadron. This work provides a general
framework for the analysis of heavy quark jet substructure observables.
