  Twisted graphene bilayers provide a versatile platform to engineer
metamaterials with novel emergent properties by exploiting the resulting
geometric moir\'{e} superlattice. Such superlattices are known to host bulk
valley currents at tiny angles ($\alpha\approx 0.3 ^\circ$) and flat bands at
magic angles ($\alpha \approx 1^\circ$). We show that tuning the twist angle to
$\alpha^*\approx 0.8^\circ$ generates flat bands away from charge neutrality
with a triangular superlattice periodicity. When doped with $\pm 6$ electrons
per moir\'e cell, these bands are half-filled and electronic interactions
produce a symmetry-broken ground state (Stoner instability) with spin-polarized
regions that order ferromagnetically. Application of an interlayer electric
field breaks inversion symmetry and introduces valley-dependent dispersion that
quenches the magnetic order. With these results, we propose a solid-state
platform that realizes electrically tunable strong correlations.
