Topological photonics has expanded our understanding of electromagnetic wave propagation and unraveled new methods of electromagnetic wave shaping. Among the various topological photonic systems, valley photonic crystal (VPC) is a highly versatile platform for constructing interfaces that supports unidirectional edge state to enable the robust topological transport of light. Although silicon VPC waveguides has demonstrated the lossless propagation of terahertz (THz) waves through multiple sharp bends, existing designs are mostly based on the standard zigzag-interface. Here, we explore interfacial topological photonics by designing a composite interface junction for an air-slot-like VPC waveguide with a 60° bend and an unchanging bearded-interface to allow the topologically protected propagation of THz waves over a 20% relative bandwidth. We employ particle swarm optimization to design the geometry of a bearded-interface silicon VPC waveguide to achieve a 42% relative bandgap and a topological edge state spanning a usable 25% relative bandwidth. Our work illustrates the prospects and challenges of interfacial topological photonics in the design of broadband silicon topological waveguides for potential applications across the electromagnetic spectrum, including the on-chip THz sixth-generation (6G) communication.