The tunable properties of halide perovskite/two dimensional (2D) semiconductor mixed-dimensional van der Waals heterostructures offer high flexibility for innovating optoelectronic and photonic devices. However, the general and robust growth of high-quality monocrystalline halide perovskite/2D semiconductor heterostructures with attractive optical properties has remained challenging. Here, we demonstrate a universal van der Waals heteroepitaxy strategy to synthesize a library of facet-specific single-crystalline halide perovskite/2D semiconductor (multi)heterostructures. The obtained heterostructures can be broadly tailored by selecting the coupling layer of interest, and can include perovskites varying from all-inorganic to organic-inorganic hybrid counterparts, individual transition metal dichalcogenides or 2D heterojunctions. The CsPbI2Br/WSe2 heterostructures demonstrate ultrahigh optical gain coefficient, reduced gain threshold and prolonged gain lifetime, which are attributed to the reduced energetic disorder. Accordingly, the self-organized halide perovskite/2D semiconductor heterostructure lasers show highly reproducible single-mode lasing with largely reduced lasing threshold and improved stability. Our findings provide a high-quality and versatile material platform for probing unique optoelectronic and photonic physics and developing further electrically driven on-chip lasers, nanophotonic devices and electronic-photonic integrated systems.