  We report the first sub-kiloparsec spatial resolution measurements of
strongly inverted gas-phase metallicity gradients in two dwarf galaxies at
$z$$\sim$2. The galaxies have stellar masses $\sim$$10^9M_\odot$, specific
star-formation rate $\sim$20 Gyr$^{-1}$, and global metallicity $12+\log({\rm
O/H})\sim8.1$ (1/4 solar), assuming the Maiolino et al. (2008) strong line
calibrations of OIII/Hb and OII/Hb. Their metallicity radial gradients are
measured to be highly inverted, i.e., 0.122$\pm$0.008 and 0.111$\pm$0.017
dex/kpc, which is hitherto unseen at such small masses in similar redshift
ranges. From the Hubble Space Telescope observations of the source nebular
emission and stellar continuum, we present the 2-dimensional spatial maps of
star-formation rate surface density, stellar population age, and gas fraction,
which show that our galaxies are currently undergoing rapid mass assembly via
disk inside-out growth. More importantly, using a simple chemical evolution
model, we find that the gas fractions for different metallicity regions cannot
be explained by pure gas accretion. Our spatially resolved analysis based on a
more advanced gas regulator model results in a spatial map of net gaseous
outflows, triggered by active central starbursts, that potentially play a
significant role in shaping the spatial distribution of metallicity by
effectively transporting stellar nucleosynthesis yields outwards. The relation
between wind mass loading factors and stellar surface densities measured in
different regions of our galaxies shows that a single type of wind mechanism,
driven by either energy or momentum conservation, cannot explain the entire
galaxy. These sources present a unique constraint on the effects of gas flows
on the early phase of disk growth from the perspective of spatially resolved
chemical evolution within individual systems.
