  We present optical transmission measurements that reveal a charge gap of 0.86
eV in the local moment antiferromagnetic insulator BaMn$_2$As$_2$, an order of
magnitude larger than previously reported. Density functional theory plus
dynamical mean field theory (DFT+DMFT) calculations correctly reproduce this
charge gap only when a strong Hund's coupling is considered. Thus,
BaMn$_2$As$_2$ is a member of a wider class of Mn pnictide compounds that are
Mott-Hund's insulators. We also present optical reflectance for metallic 2% K
doped BaMn$_2$As$_2$ that we use to extract the optical conductivity at
different temperatures. The optical conductivity $\sigma_1$($\omega$) exhibits
a metallic response that is well described by a simple Drude term. Both
$\sigma$($\omega$$\rightarrow$0, T) and $\rho$(T) exhibit Fermi liquid
temperature dependencies. From these measurements, we argue that a more
strongly correlated Hund's metal version of the parent compounds of the iron
pnictide superconductors has not yet been realized by doping this class of
Hund's insulators.
