We present observations obtained from 1-4 microns simultaneously (resolving power of order 100) of a lunar occultation of the AGB star OH06.86-1.5 using a high speed spectrophotometer, pMIRAS, developed at the University of Texas McDonald Observatory. The broad wavelength coverage extends from the 1 micron region where the flux is dominated by the central star to the 4 micron region where it is dominated by emission from the dust shell produced by mass loss from the central star. This broad and inclusive wavelength coverage allows us to produce models for the dust shell that constrain the location and density of the shell. We fit both the overall energy distribution as well as the roughly 50 independent Fresnel fringe light curves as a function of wavelength. Although lunar occultation observations have a number of practical limitations, the high angular resolution afforded by this technique is a valuable complement to separated-aperture interferometry in the infrared.