The interest in Fe-chalcogenide unconventional superconductors is intense after the critical temperature of FeSe was reported enhanced by more than one order of magnitude in the monolayer limit at the interface to an insulating oxide substrate. In heterostructures comprising interfaces of FeSe with topological insulators, additional interesting physical phenomena is predicted to arise e.g. in form of {it topological superconductivity}. So far superconductive properties of Fe-chalcogenide monolayers were mostly studied by local scanning tunneling spectroscopy experiments, which can detect pseudo-gaps in the density of states as an indicator for Cooper pairing. Direct macroscopic transport properties which can prove or falsify a superconducting phase were rarely reported due to the difficulty to grow films with homogeneous material properties. Here we report on a promising growth method to fabricate continuous carpets of monolayer thick FeSe on molecular beam epitaxy grown Bi$_2$Se$_3$ topological insulator thin films. In contrast to previous works using atomically flat cleaved bulk Bi$_2$Se$_3$ crystal surfaces we observe a strong influence of the high step-edge density (terrace width about 10~nm) on MBE-grown Bi$_2$Se$_3$ substrates, which significantly promotes the growth of coalescing FeSe domains with small tetragonal crystal distortion without compromising the underlying Bi$_2$Se$_3$ crystal structure.
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