High‐temperature cuprate superconductors based van der Waals (vdW) heterostructures hold high technological promise. One of the obstacles hindering their progress is the detrimental effect of disorder on the properties of the vdW‐devices‐based Josephson junctions (JJs). Here, a new method of fabricating twisted vdW heterostructures made of Bi2Sr2CuCa2O8+δ, crucially improving the JJ characteristics and pushing them up to those of the intrinsic JJs in bulk samples, is reported. The method combines cryogenic stacking using a solvent‐free stencil mask technique and covering the interface by insulating hexagonal boron nitride crystals. Despite the high‐vacuum condition down to 10−6 mbar in the evaporation chamber, the interface appears to be protected from water molecules during the in situ metal deposition only when fully encapsulated. Comparing the current–voltage curves of encapsulated and unencapsulated interfaces, it is revealed that the encapsulated interfaces’ characteristics are crucially improved, so that the corresponding JJs demonstrate high critical currents and sharpness of the superconducting transition comparable to those of the intrinsic JJs. Finally, it is shown that the encapsulated heterostructures are more stable over time.