  We present our investigations on the superconducting properties of monolayers
of FeSe$_{0.5}$Te$_{0.5}$ grown on the 3D topological insulator
Bi$_{2}$Se$_{1.2}$Te$_{1.8}$ using low temperature scanning tunneling
spectroscopy (STS). While the morphology and the overall transition temperature
resemble those of similarly doped bulk crystals, the spatially resolved
spectroscopic data at 1.1K shows a much larger spatial inhomogeneity in the
superconducting energy gaps. Despite the gap inhomogeneity all the spectra can
be fitted with a two-fold anisotropic s-wave gap function. The two-fold nature
of the gap symmetry is evident from the Bogoliubov quasiparticle interference
(QPI) pattern which shows distinct C$_{2}$ symmetric scattering intensities. We
argue that the gap inhomogeneity emerges as a result of intrinsic disorder in
our system similar to disordered conventional superconductors. Even though most
of our findings clearly differ from the current understanding of the
corresponding bulk system, it provides an ideal platform to study
unconventional superconductivity in Fe chalcogenides thinned down to a single
layer and in close proximity to a topological insulator.
