  We initiate the application of Hamiltonian Truncation methods to solve
strongly coupled QFTs in $d=2+1$. By analysing perturbation theory with a
Hamiltonian Truncation regulator, we pinpoint the challenges of such an
approach and propose a way that these can be addressed. This enables us to
formulate Hamiltonian Truncation theory for $\phi^4$ in $d=2+1$, and to study
its spectrum at weak and strong coupling. The results obtained agree well with
the predictions of a weak/strong self-duality possessed by the theory. The
$\phi^4$ interaction is a strongly relevant UV divergent perturbation, and
represents a case study of a more general scenario. Thus, the approach
developed should be applicable to many other QFTs of interest.
