Periodic structures of silicon are of interest in quantum-dot-based applications because of their unique optical and electronic properties. We report on the fabrication of stable quasi-ordered Si nanocluster arrays on the moiré of a hexagonal boron nitride (h-BN) monolayer on Ir(111). The h-BN monolayer promotes the growth of regular Si nanoclusters at 130 K and electronically decouples the clusters from the underlying metallic substrate. Using scanning tunneling microscopy and spectroscopy, we have investigated the cluster binding sites, their electronic structure, and their thermal stability. We find that the clusters display a size-dependent bandgap and that they are stable up to 577 K, after which cluster coalescence degrades the arrays.