  We present a first calculation of the heavy flavor contribution to the
longitudinally polarized deep-inelastic scattering structure function
$g_1^{Q}$, differential in the transverse momentum or the rapidity of the
observed heavy quark $Q$ or antiquark $\overline Q$. All results are obtained
at next-to-leading order accuracy in QCD within the framework of a newly
developed parton-level Monte Carlo generator that also allows one to study
observables associated with the produced heavy quark pair such as its invariant
mass distribution or its correlation in azimuthal angle. First phenomenological
studies are carried out for various heavy quark distributions in a kinematic
regime relevant for a future Electron-Ion Collider with a particular emphasis
on the expected size of the corresponding double-spin asymmetries and their
sensitivity to the still poorly constrained helicity gluon distribution.
Theoretical uncertainties associated with the choice of the factorization scale
are discussed for selected observables.
