Cluster varieties associated to skew-symmetric matrices are moduli spaces of rank one microlocal sheaves on Lagrangian skeletons of certain exact symplectic manifolds. The symplectic manifolds are obtained from cotangent bundles of surfaces by attaching Weinstein handles along Legendrians at infinity. The skew symmetric matrix is the intersection pairing on the images of the Legendrians in the surface. Cluster variables name the Lagrangian disks at the core of the handles, and mutation is Lagrangian disk surgery.