Globular clusters are the oldest conglomerates of stars in our Galaxy and can be useful laboratories to test theories from stellar evolution to cosmology. In this paper, we present a new method to estimate the absolute age of a globular cluster from observations of its brown dwarfs. The transition region between the end of the main sequence and the brown dwarf regime is characterized by a dearth of objects as function of magnitude. The brightest of the cooling brown dwarfs is easily identified by an increase in density in the color-magnitude diagram as you go fainter in magnitudes, and these brightest brown dwarfs get fainter with age. By identifying the brightest brown dwarfs, it is thus possible to determine the age of a globular cluster within a 1 Gyr precision with four-sigma confidence. This new method, which is independent of current methods of age estimation and which does not rely on the knowledge of the cluster's distance from Earth, will become feasible thanks to the high spatial resolution and incredible infrared sensitivity of the James Webb Space Telescope.