We developed novel techniques to fabricate atomically thin Bi_{2.1}Sr_{1.9}CaCu_{2.0}O_{8+δ} van der Waals heterostructures down to two unit cells while maintaining a transition temperature T_{c} close to the bulk, and carry out magnetotransport measurements on these van der Waals devices. We find a double sign change of the Hall resistance R_{xy} as in the bulk system, spanning both below and above T_{c}. Further, we observe a drastic enlargement of the region of sign reversal in the temperature-magnetic field phase diagram with decreasing thickness of the device. We obtain quantitative agreement between experimental R_{xy}(T,B) and the predictions of the vortex dynamics-based description of Hall effect in high-temperature superconductors both above and below T_{c}.