We analyze tunneling of non-Abelian quasiparticles between the edges of a quantum Hall droplet at Landau level filling fraction nu=5/2, assuming that the electrons in the first excited Landau level organize themselves in the non-Abelian Moore-Read Pfaffian state. We formulate a bosonized theory of the modes at the two edges of a Hall bar; an effective spin-1/2 degree of freedom emerges in the description of a point contact. We show how the crossover from the high-temperature regime of weak quasiparticle tunneling between the edges of the droplet, with 4-terminal R_{xx} scaling as T^{-3/2}, to the low-temperature limit, with R_{xx} - h/(10 e^2) scaling as -T^4, is closely related to the two-channel Kondo effect. We give a physical interpretation for the entropy of ln(2sqrt{2}) which is lost in the flow from the ultraviolet to the infrared.
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