We experimentally demonstrate a robust Si-photonic waveguide architecture that realizes dynamically encircling an exceptional point (EP) in the optical domain and broadband asymmetric modal transmission as an essential consequence. The structure consists of a pair of coupled channel waveguides and an adjacent slab-waveguide patch that enable precise lithographic controls on the phase velocities and radiation rates of the guided photonic modes. Complex modal index and inter-mode coupling constant profiles required for the encircling-an-EP parametric control are precisely coded in the geometry of those elements. The device created on this basis induces the symmetry-exchanging adiabatic state flip for one transmission direction and symmetry-preserving anti-adiabatic state-jump for the transmission in the opposite direction. In fabrication, we use a state-of-the-art electron-beam lithography for creating mm-long devices with nm-scale transversal precision. A comprehensive spectral measurement for the intensity and phase distributions of the transmitted optical states is obtained with a specially designed phase-sensitive infrared microscopy integrated with a tunable diode-laser system and spectrum analyzer. On this basis, we confirm in the experiment the highly asymmetric modal transmission persisting over a broad spectral band exceeding 100 nm in the telecommunications window around 1,550 nm. Hence, we establish a substantive experimental step toward broadband non-reciprocal photonic devices based on the unique non-Hermitian dynamics.