  We expand the concept of frustration in Mott insulators and quantum spin
liquids to metals with flat bands. We show that when inter-orbital hopping
$t_2$ dominates over intra-orbital hopping $t_1$, in a multiband system with
strong spin-orbit coupling $\lambda$, electronic states with a narrow bandwidth
$W\sim t_2^2/\lambda$ are formed compared to a bandwidth of order $t_1$ for
intra-orbital hopping. We demonstrate the evolution of the electronic
structure, Berry phase distributions for time-reversal and inversion breaking
cases, and their imprint on the optical absorption, in a tight binding model of
$d$-orbital hopping on a honeycomb lattice. Going beyond quantum Hall effect
and twisted bilayer graphene, we provide an alternative mechanism and a richer
materials platform for achieving flat bands poised at the brink of
instabilities toward novel correlated and fractionalized metallic phases.
