There aren't any. Hausdorff spaces are <a href="https://ncatlab.org/nlab/show/sober+topological+space">sober spaces</a>. If $X, Y$ are sober, then every locale map $\mathcal{O}(Y) \to \mathcal{O}(X)$, i.e., every poset map between their topologies that preserves finite meets and arbitrary joins, arises from a uniquely determined continuous map $X \to Y$. It follows that a poset isomorphism $\mathcal{O}(X) \cong \mathcal{O}(Y)$, being a locale isomorphism, arises from a homeomorphism between the spaces.