Cherenkov detectors enable a valuable tool to identify high-energy particles. However, their sensitivity and momentum coverage are limited by the refractive index of host materials. Especially, identifying particles with energy above multiple gigaelectronvolts requires host materials with a near-unity refractive index, which are limited to bulky gas chambers. Overcoming this fundamental material limit is important for future particle detectors yet remains a long-standing challenge. Here, we propose a different paradigm for Cherenkov detectors that utilizes the broadband angular filter made from stacks of variable one-dimensional photonic crystals. Owing to the Brewster effect, the angular filter is transparent only to Cherenkov photons from a precise incident angle. Particle identification is achieved by mapping each Cherenkov angle to the peak-intensity position of transmitted photons in the detection plane. Such angular filtering effect, although decreases the photon number collected in the detection plane, enables the realization of a non-dispersive pseudo refractive index over the entire visible spectrum. Moreover, the pseudo refractive index can be flexibly designed to different values close to unity. Our angular-selective Brewster paradigm offers a feasible solution to implement compact and highly sensitive Cherenkov detectors especially in beam lines with a small angular divergence using regular dielectrics.