We have studied the interplay of a giant spin-orbit splitting and of quantum confinement in artificial Bi-Ag-Si trilayer structures. Angle-resolved photoelectron spectroscopy reveals the formation of a complex spin-dependent gap structure, which can be tuned by varying the thickness of the Ag buffer layer. This provides a means to tailor the electronic structure at the Fermi energy, with potential applications for silicon-compatible spintronic devices.