  The H1 Collaboration at HERA reports the first measurement of groomed event
shape observables in deep inelastic electron-proton scattering (DIS) at
$\sqrt{s}=319$ GeV, using data recorded between the years 2003 and 2007 with an
integrated luminosity of $351$ pb$^{-1}$. Event shapes provide incisive probes
of perturbative and non-perturbative QCD. Grooming techniques have been used
for jet measurements in hadronic collisions; this paper presents the first
application of grooming to DIS data. The analysis is carried out in the Breit
frame, utilizing the novel Centauro jet clustering algorithm that is designed
for DIS event topologies. Events are required to have squared momentum-transfer
$Q^2 > 150$ GeV$^2$ and inelasticity $ 0.2 < y < 0.7$. We report measurements
of the production cross section of groomed event 1-jettiness and groomed
invariant mass for several choices of grooming parameter. Monte Carlo model
calculations and analytic calculations based on Soft Collinear Effective Theory
are compared to the measurements.
