Crystalline solids can become band insulators due to fully filled bands, or Mott insulators due to strong electronic correlations. While Mott insulators can theoretically occur in systems with an even number of electrons per unit cell, distinguishing them from band insulators experimentally has remained a longstanding challenge. In this work, we present a unique momentum-resolved signature of a dimerized Mott-insulating phase in the experimental spectral function of Nb₃Br₈: the top of the highest occupied band along the out-of-plane direction k_z has a momentum-space separation Δk_z = 2π/d, whereas that of a band insulator is less than π/d, where d is the average interlayer spacing. Identifying Nb₃Br₈ as a Mott insulator is crucial to understand its role in the field-free Josephson diode effect. Moreover, our method could be extended to other van der Waals systems where tuning interlayer coupling and Coulomb interactions can drive a band- to Mott-insulating transition.