Cut-cell methods for unsteady flow problems can greatly simplify the grid generation process and al- low for high-fidelity simulations on complex geometries. Historically, however, cut-cell methods have been limited to low orders of accuracy. It is the conjecture of the authors that this has been driven, by the variety of procedures typically introduced to evaluate derivatives in a stable manner near the highly irregular embedded geometry. Indeed, even on a uniform mesh, it is non-trivial to derive high-order numerical boundary schemes to be used near the wall. Recently, the authors have developed a simulation based optimization technique[1] that allowed for the construction of high-order stable numerical bound- ary schemes (NBS) for uniform meshes. The work was further refined by reframing the problem in the context of energy stability [4]. Pursuing a finite-differences based cut-cell approach (also referred to as an ”embedded boundary” or ”Cartesian grid” method), allowed for formulating the small cell problem encountered by cut-cell methods as an NBS problem. Coupled with a truncation error matching idea, this simulation based optimization strategy was applied to cut-cells [2] resulting in conservative 4th order approximations to hyperbolic problems without the addition of numerical dissipation as well as 8th order approximations for elliptic and parabolic systems. This work was again refined by reframing the problem in the context of energy stability [3], allowing for the construction of high-order cut-cell approximations with provable stability properties. In the present work, we will discuss our efforts to expand the method to systems with diverse boundary conditions such that it can be adopted for high fidelity flow simulations.