The production of high-quality two-dimensional (2D) materials is essential for the ultimate performance of single layers and their hybrids. Hexagonal boron nitride (h-BN) is foreseen to become the key 2D hybrid and packaging material since it is insulating, impermeable, flat, transparent, and chemically inert, though it is difficult to attain in ultimate quality. Here, a scheme is reported for producing single layer h-BN that shows higher quality in view of mosaicity and strain variations than material from chemical vapor deposition (CVD). We delaminate CVD h-BN from Rh(111) and transfer it to a clean metal surface. The twisting angle between BN and the second substrate yields metastable moiré structures. Annealing above 1000 K leads to 2D distillation, i.e., catalyst-assisted BN sublimation from the edges of the transferred layer and subsequent condensation into superior quality h-BN. This provides a way for 2D material production remote from CVD instrumentation.