  We give a new geometric construction of the big projective module in the
principal block of the BGG category $\mathscr{O}$, or rather the corresponding
$\mathscr{D}$-module on the flag variety. Namely, given a one-parameter family
of nondegenerate additive characters of the unipotent radical of a Borel
subgroup which degenerate to the trivial character, there is a corresponding
one-parameter family of Whittaker sheaves. We show that the unipotent nearby
cycles functor applied to this family yields the big projective
$\mathscr{D}$-module.
