  We use a direct QCD approach to carry out the next-to-next-to-leading
logarithmic (NNLL) resummation for observables groomed with the modified
mass-drop tagger (Soft Drop $\beta=0$). We focus on observables which are
additive given an arbitrary number of soft-collinear emissions. For this class
of observables, we arrange the structure of the NNLL terms into two distinct
categories. The first defines a simplified inclusive tagger, whereby the NNLL
collinear structure is directly related to ungroomed observables. The second
defines a clustering correction which takes a particularly simple form when the
Cambridge-Aachen (C/A) algorithm is used to cluster the jets. We provide, in
addition to the QCD resummation of groomed jet mass, the first NNLL resummed
predictions, matched to NLO, for a range of groomed jet angularities with mMDT
grooming. Moreover, we also include for the first time in the same calculation,
finite $z_{\mathrm{cut}}$ effects computed at NLL level alongside the small
$z_{\mathrm{cut}}$ NNLL results which simultaneously improves upon both of the
calculations used for groomed jet mass phenomenological studies to date. While
for simplicity we focus on $e^{+}e^{-}$ collisions, the essential NNLL
resummation we develop is process independent and hence with the appropriate
NLO matching our results are also applicable for hadron collider phenomenology.
