  We construct the first examples of normal subgroups of mapping class groups
that are isomorphic to non-free right-angled Artin groups. Our construction
also gives normal, non-free right-angled Artin subgroups of other groups, such
as braid groups and pure braid groups, as well as many subgroups of the mapping
class group, such as the Torelli subgroup. Our work recovers and generalizes
the seminal result of Dahmani-Guirardel-Osin, which gives free, purely
pseudo-Anosov normal subgroups of mapping class groups. We give two
applications of our methods: (1) we produce an explicit proper normal subgroup
of the mapping class group that is not contained in any level $m$ congruence
subgroup, and (2) we produce an explicit example of a pseudo-Anosov mapping
class with the property that all of its even powers have free normal closure
and its odd powers normally generate the entire mapping class group. The
technical theorem at the heart of our work is a new version of the windmill
apparatus of Dahmani-Guirardel-Osin, which is tailored to the setting of group
actions on the projection complexes of Bestvina-Bromberg-Fujiwara.
