  We prove the Strominger--Yau--Zaslow and topological mirror symmetries for
parabolic Hitchin systems of types B and C. In contrast to type A, a geometric
reinterpretation of Springer duality is necessary. Furthermore, unlike
Hitchin's construction in the non-parabolic case, the map between generic
fibers in type B and C needs more analysis due to the change of partitions of
Springer dual nilpotent orbits, which is the main difficulty in this article.
To tackle this challenge, we first construct and study the geometry of the
generic Hitchin fibers of moduli spaces of Higgs bundles associated to the
nilpotent orbit closures. Then we study their relation with the generic Hitchin
fibers of parabolic Hitchin systems. Along this way, we establish intriguing
connections between Springer duality, Kazhdan--Lusztig maps, and singularities
of spectral curves, and uncover a new geometric interpretation of Lusztig's
canonical quotient.
