  We investigate the electronic structure and the optical absorption onset of
close-to-30\degree twisted hexagonal boron nitride bilayers. Our study is
carried out with a purposely developed tight-binding model validated against
DFT simulations. We demonstrate that approaching 30\degree (quasicrystal
limit), all bilayers sharing the same moir\'e supercell develop identical band
structures, irrespective of their stacking sequence. This band structure
features a bundle of flat bands laying slightly above the bottom conduction
state which is responsible for an intense peak at the onset of the absorption
spectrum. These results suggest the presence of strong, stable and
stacking-independent excitons in boron nitride 30\degree-twisted bilayers. By
carefully analyzing the electronic structure and its spatial distribution, we
elucidate the origin of these states as moir\'e-induced K-valley scattering due
to interlayer B$-$B coupling. We take advantage of the the physical
transparency of the tight-binding parameters to derive a simple triangular
model based on the B sublattice that accurately describes the emergence of the
bundle. Being our conclusions very general, we predict that a similar bundle
should emerge in other close-to-30{\degree} bilayers, like transition metal
dichalcogenides, shedding new light on the unique potential of 2D materials.
