  We explore transport across an ultra-small Quantum Hall Island (QHI) formed
by closed quan- tum Hall edge states and connected to propagating edge channels
through tunnel barriers. Scanning gate microscopy and scanning gate
spectroscopy are used to first localize and then study a single QHI near a
quantum point contact. The presence of Coulomb diamonds in the spectroscopy
con- firms that Coulomb blockade governs transport across the QHI. Varying the
microscope tip bias as well as current bias across the device, we uncover the
QHI discrete energy spectrum arising from electronic confinement and we extract
estimates of the gradient of the confining potential and of the edge state
velocity.
