  We introduce a novel category of observables known as the Semi-Inclusive
Energy Correlators (SIECs), an extension of the recently proposed nucleon
energy correlator to integrate a new element, the fragmenting energy
correlation function. These SIECs gauge the correlation between the examined
hadron and the surrounding radiations, providing a comprehensive tomography of
the radiative patterns originating from initial state radiation or parton
fragmentation. As such, they could function as the generating functions for
numerous kinematic distributions. To illustrate, we find a direct relation
between the transverse momentum moments (TMMs) of the transverse
momentum-dependent (TMD) distributions and the SIECs. We demonstrate how the
TMMs of the TMD parton distributions and the fragmentation functions can be
distinctively derived from the nucleon energy correlator and the fragmenting
energy correlator, respectively, without enforcing the back-to-back kinematics.
