Electronic correlations are crucial to the low energy physics of metallic systems with localized $d$ and $f$ states; however, their effect on band insulators and semiconductors is typically negligible. Here, we measure the electronic structure of the half-Heusler compound FeVSb, a band insulator with filled shell configuration of 18 valence electrons per formula unit ($s^2 p^6 d^{10}$). Angle-resolved photoemission spectroscopy (ARPES) reveals a mass renormalization of $m^{*}/m_{bare}= 1.4$, where $m^{*}$ is the measured effective mass and $m_{bare}$ is the mass from density functional theory (DFT) calculations with no added on-site Coulomb repulsion. Our measurements are in quantitative agreement with dynamical mean field theory (DMFT) calculations, highlighting the many-body origin of the mass renormalization. This mass renormalization lies in dramatic contrast to other filled shell intermetallics, including the thermoelectric materials CoTiSb and NiTiSn; and has a similar origin to that in FeSi, where Hunds coupling induced fluctuations across the gap can explain a dynamical self-energy and correlations. Our work calls for a re-thinking of the role of correlations and Hunds coupling in intermetallic band insulators.