Lattice QCD has become an essential tool for studying the hadron-hadron interaction from the first principles. However, when extracting infinite-volume scattering parameters from finite-volume energy levels, the traditional Lüscher formula encounters limitations due to the left-hand cut induced by long-range interactions such as the one-pion exchange. In this work, we propose an alternative approach based on chiral effective field theory combined with a Hamiltonian method in the plane wave basis. By solving a Schrödinger-like equation in the finite volume, our method connects the finite-volume energy spectrum with infinite-volume observables, while systematically incorporating the long-range physics and solving the left-hand cut problem. The use of the plane wave basis mitigates issues related to partial wave mixing. Our numerical results for $DD^*$ scattering at $m_\pi \approx$ 280 MeV demonstrate that this approach overcomes the limitations of the Lüscher method and points towards a resonance interpretation of the $T_{cc}(3875)$ state, as opposed to the virtual state predicted by traditional analyses.