As the rising renewable energy demands and lithium scarcity, developing high-capacity anode materials to improve the energy density of potassium-based batteries (PBBs) is increasingly crucial. In this work, a unique orderly multilayered growth (OMLG) mechanism on a 2D-Ca2Si monolayer is theoretically demonstrated for potassium storage by first-principles calculations. The global-energy-minimum Ca2Si monolayer is a semiconductor with isotropic mechanical properties and remarkable electrochemical properties, such as a low potassium ion migration energy barrier of 0.07eV and a low open circuit voltage ranging from 0.224 to 0.003V. Most notably, 2D-Ca2Si demonstrates an ultrahigh theoretical specific capacity of 5459mAhg-1 and a total specific capacity of 610mAhg-1, reaching up to 89% of the capacity of a potassium metal anode. Remarkably, the OMLG mechanism facilitates stable, dendrite-free deposition of hcp-K metal layers on the 2D-Ca2Si surface, where the ultrahigh and gradually converging lattice match as the layers increase is the key to achieving theoretically near-infinite growth. The study theoretically demonstrates the Ca2Si monolayer a highly promising anode material, and offers a novel potassium storage strategy for designing 2D anode materials with high specific capacity, rapid potassium-ion migration, and good safety.