Poincaré–Einstein metrics play an important role in geometric analysis and mathematical physics, yet constructing new examples beyond the perturbative regime is difficult. In this talk, I will describe a class of four-dimensional Poincaré–Einstein manifolds that are conformal to Kähler metrics. These metrics admit a natural symmetry generated by a Killing field, which reduces the Einstein equations to a Toda-type system. This approach leads to existence and uniqueness results in the case of complex line bundles over surfaces of genus at least one. The construction produces large-scale, infinite-dimensional families of new Poincaré–Einstein metrics with conformal infinities of non-positive Yamabe type. This is joint work with Mingyang Li.