  We report the first double-differential cross section measurement of
neutral-current neutral pion (NC$\pi^0$) production in neutrino-argon
scattering, as well as single-differential measurements of the same channel in
terms of final states with and without protons. The kinematic variables of
interest for these measurements are the $\pi^0$ momentum and the $\pi^0$
scattering angle with respect to the neutrino beam. A total of 4971 candidate
NC$\pi^0$ events fully-contained within the MicroBooNE detector are selected
using data collected at a mean neutrino energy of $\sim 0.8$ GeV from
$6.4\times10^{20}$ protons on target from the Booster Neutrino Beam at the
Fermi National Accelerator Laboratory. After extensive data-driven model
validation to ensure unbiased unfolding, the Wiener-SVD method is used to
extract nominal flux-averaged cross sections. The results are compared to
predictions from commonly used neutrino event generators, which tend to
overpredict the measured NC$\pi^0$ cross section, especially in the 0.2-0.5
GeV/c $\pi^0$ momentum range, at forward scattering angles, and when at least
one proton is present in the final state. These measurements show sensitivity
to a variety of features that complicate the description of NC$\pi^0$
production including the form factors describing the elementary neutrino
interaction and the final state interactions of the outgoing particles in the
residual argon nucleus. This data will help improve the modeling of NC$\pi^0$
production, which represents a major background in measurements of
charge-parity violation in the neutrino sector and in searches for new physics
beyond the Standard Model.
