  We propose an observable which involves measuring the properties (transverse
momentum $p_{h\perp}$ and energy fraction $z_h$) of an identified hadron inside
a groomed jet. The jet is identified with an anti-kT/CA algorithm and is
groomed by implementing the modified mass drop procedure with an energy cut-off
parameter $z_{cut}$. The transverse momentum of the hadron inside the jet is
measured with respect to the groomed jet axis. We obtain a factorization
theorem in the framework of Soft Collinear Effective Theory (SCET), to define a
Transverse Momentum Dependent Fragmenting Jet Function (TMDFJF). The TMDFJF is
factorized into collinear and collinear soft modes by matching onto SCET$_+$.
We resum large logarithms in $E_J/p_{h\perp}$, where $E_J$ is the ungroomed jet
energy, to NLL accuracy and apply this formalism for computing the shape of the
$p_{h\perp}$ distribution of a pion produced in an $e^+ +e^-$ collision. We
observe that the introduction of grooming makes this observable insensitive to
non-global logarithms and particularly sensitive to non-perturbative physics of
the transverse momentum dependent evolution at low values of $p_{h\perp}$,
which can be probed in the variation of the cut-off parameter $z_{cut}$ of the
groomer. We discuss how this observable can be used to distinguish between
non-perturbative models that describe universal TMD evolution and provide a
window into the three dimensional structure of hadrons.
