  We study an effective model of two interacting species of bosons in two
dimensions, which is amenable to sign problem free Monte Carlo simulations. In
addition to conventional ground states, we access a paired superfluid which is
also a topological phase, protected by the remaining $U(1) \times \mathbb{Z}_2$
symmetry. This phase arises from the condensation of a composite object, the
bound state of vortices and anti-vortices of one species, to a boson of the
second species. We introduce a bulk response function, the Ising analog of the
quantized Hall effect, to diagnose the topological phase. The interplay of
broken symmetry and topology leads to interesting effects such as fractionally
charged vortices in the paired superfluid. Possible extensions towards
realistic models of cold atomic bosons are discussed.
