Essentially Normal Composition Operators on $H^2$

We prove a simple criterion for essential normality of composition operators on the Hardy space induced by maps in a reasonably large class of analytic self-maps of the unit disk. By combining this criterion with boundary Carath'{e}odory-Fej'{e}r interpolation theory, we exhibit a parametrization for all rational self-maps of the unit disk which induce essentially normal composition operators.