In this paper we develop an optimality-based disturbance rejection control framework for nonlinear cascade systems with bounded energy (square-integrable) L-2 disturbances. Specifically, using a nonlinear-non-quadratic disturbance rejection optimal control framework we develop a family of globally stabilizing generalized backstepping controllers parametrized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Hamilton-Jacobi-Isaacs equation for the controlled system and thus guarantees both optimality and stability. In addition, the resulting optimal controller guarantees that the closed-loop system is non-expansive (gain bounded).