  In spacetimes with asymmetric extra dimensions, cosmic neutrino interactions
may be extraordinarily enhanced by p-brane production. Brane formation and
decay may then initiate showers deep in the Earth's atmosphere at rates far
above the standard model rate. We explore the p-brane discovery potential of
cosmic ray experiments. The absence of deeply penetrating showers at AGASA
already provides multi-TeV bounds on the fundamental Planck scale that
significantly exceed those obtained from black hole production in symmetric
compactification scenarios. This sensitivity will be further enhanced at the
Auger Observatory. We also examine the possibility that p-brane formation
resolves the GZK paradox. For flat compactifications, astrophysical bounds
exclude this explanation. For warped scenarios, a solution could be consistent
with the absence of deep showers only for extra dimensions with fine-tuned
sizes well below the fundamental Planck length. In addition, it requires
moderately penetrating showers, so far not reported, and ~100% modifications to
standard model phenomenology at 100 GeV energies.
