We present a study of the peculiar Type Ia supernova 2001ay (SN 2001ay). The defining features of its peculiarity are: high velocity, broad lines, and a fast rising light curve, combined with the slowest known rate of decline. It is one magnitude dimmer than would be predicted from its observed value of Delta-m15, and shows broad spectral features. We base our analysis on detailed calculations for the explosion, light curves, and spectra. We demonstrate that consistency is key for both validating the models and probing the underlying physics. We show that this SN can be understood within the physics underlying the Delta-m15 relation, and in the framework of pulsating delayed detonation models originating from a Chandrasekhar mass, white dwarf, but with a progenitor core composed of 80% carbon. We suggest a possible scenario for stellar evolution which leads to such a progenitor. We show that the unusual light curve decline can be understood with the same physics as has been used to understand the Delta-m15 relation for normal SNe Ia. The decline relation can be explained by a combination of the temperature dependence of the opacity and excess or deficit of the peak luminosity, alpha, measured relative to the instantaneous rate of radiative decay energy generation. What differentiates SN 2001ay from normal SNe Ia is a higher explosion energy which leads to a shift of the Ni56 distribution towards higher velocity and alpha < 1. This result is responsible for the fast rise and slow decline. We define a class of SN 2001ay-like SNe Ia, which will show an anti-Phillips relation.