The derivation of hydrodynamic equations from kinetic theory has been a central problem since the inception of the Boltzmann equation. Early systematic closures were developed through asymptotic expansions in the Knudsen number, most prominently the Chapman–Enskog expansion [1, 2], which organizes the kinetic distribution as a perturbation about a local Maxwellian manifold. At leading orders this procedure yields the compressible Euler equations and the Navier–Stokes–Fourier system, establishing a quantitative link between microscopic collision dynamics and macroscopic transport coefficients. Despite this success, it has long been recognized that higher-order truncations of the Chapman–Enskog expansion, such as the Burnett and super-Burnett equations, suffer from fundamental deficiencies. These include loss of well-posedness, linear instability of equilibrium states, and unphysical behavior at short wavelengths, even though the underlying Boltzmann dynamics remains stable and entropy-dissipating. These pathologies are now understood as consequences of finite-order truncation of an asymptotic expansion that is not uniformly valid across scales, and of the delicate interaction between hydrodynamic and kinetic modes. As a result, much subsequent work has focused on regularized Burnett models, moment closures, and alternative formulations of extended hydrodynamics designed to restore stability while retaining higher-order accuracy. The success of these approaches is debatable and there is room for new ideas. In this work, we pursue the closure problem for the Boltzmann equation from the perspective of the Variational Multiscale Method which provides a systematic way to decompose kinetic dynamics into resolved hydrodynamic components and unresolved fine-scale corrections. By modeling the influence of unresolved kinetic scales on the resolved variables in a variationally consistent manner, this approach offers a pathway to stable hydrodynamic closures that retain essential non-equilibrium effects while avoiding the classical instabilities associated with higher-order Chapman–Enskog expansions.