We theoretically investigate twisted structures where each layer is composed of a strongly correlated material. In particular, we study a twisted t-J model of cuprate multilayers within the slave-boson mean field theory. This treatment encompasses the Mott physics at small doping and self consistently generates d-wave pairing. Furthermore, including the correct inter-layer tunneling form factor consistent with the symmetry of the Cu d x 2 −y 2 orbital proves to be crucial for the phase diagram. We find spontaneous time reversal (T) breaking around twist angle of 45 • , although only in a narrow window of twist angles. Moreover, the gap obtained is small and the Chern number vanishes, implying a non-topological superconductor. At smaller twist angles, driving an interlayer current however can lead to a gapped topological phase. The energy-phase relation of the interlayer Josephson junction displays notable double-Cooper-pair tunneling which dominates around 45 o . The twist angle dependence of the Josephson critical current and the Shapiro steps are consistent with recent experiments. Utilizing the moiré structure as a probe of correlation physics, in particular of the pair density wave state, is discussed.1 Strictly speaking, the oxygen p orbital is also involved in hole doped cuprate, forming the Zhang-Rice singlet. However, the active Zhang-Rice singlet has the same symmetry as the Cu d x 2 −y 2 orbital and does not change our analysis.