  We introduce a superpotential for partial flag varieties of type $A$. This is
a map $W: Y^\circ \to \mathbb{C}$, where $Y^\circ$ is the complement of an
anticanonical divisor on a product of Grassmannians. The map $W$ is expressed
in terms of Pl\"ucker coordinates of the Grassmannian factors. This
construction generalizes the Marsh--Rietsch Pl\"ucker coordinate mirror for
Grassmannians. We show that in a distinguished cluster chart for $Y$, our
superpotential agrees with earlier mirrors constructed by Eguchi--Hori--Xiong
and Batyrev--Ciocan-Fontanine--Kim--van Straten. Our main tool is quantum
Schubert calculus on the flag variety.
