A long standing obstacle to realizing highly sought on-chip monolithic solid state quantum optical circuits has been the lack of a starting platform comprising scalable spatially ordered and spectrally uniform on-demand single photon sources (SPSs) buried under a planar surface. In this paper, we report on the first realization of planarized SPS arrays based on a unique class of shape-controlled single quantum dots (SQDs) synthesized on mesa top (dubbed MTSQDs) using substrate-encoded size-reducing epitaxy (SESRE) on spatially regular arrays of patterned nanomesas with edge orientation chosen to drive symmetric adatom migration from the nanomesa sidewalls to the top, thereby enabling spatially selective growth. Specifically, on GaAs(001) square nanomesas with edges along 100, we synthesized binary GaAs/InAs/GaAs MTSQDs emitting around 1120 nm with 1.8 nm standard deviation and single photon emission purity >99.5%. SESRE based MTSQDs are shown for the first time to lend themselves to planarization of the surface morphology when grown on pedestal shape mesas. We demonstrate that the planarizing overgrowth process over arrays of InGaAs SQDs largely maintains the SQDs' high single photon emission purity (>98%) and spectral uniformity (∼5 nm). Such planarized SQD arrays offer the long-sought platform for on-chip integration with light manipulating structures to realize quantum optical circuits.