  We investigate the $\mathbb{T}^2$-quotient of a torsion free
$Spin(7)$-structure on an $8$-manifold under the assumption that the quotient
$6$-manifold is K\"ahler. We show that there exists either a Hamiltonian $S^1$
or $\mathbb{T}^2$ action on the quotient preserving the complex structure.
Performing a K\"ahler reduction in each case reduces the problem of finding
$Spin(7)$ metrics to studying a system of PDEs on either a $4$- or $2$-manifold
with trivial canonical bundle, which in the compact case corresponds to either
$\mathbb{T}^4$, a K3 surface or an elliptic curve. By reversing this
construction we give infinitely many new explicit examples of $Spin(7)$
holonomy metrics. In the simplest case, our result can be viewed as an
extension of the Gibbons-Hawking ansatz.
