When two superconductors are connected across a ferromagnet, the spin configuration of the transferred Cooper pairs can be modulated due to magnetic exchange interaction. The resulting supercurrent can reverse its sign across the Josephson junction (JJ) [1-4]. Here we demonstrate Josephson phase modulation in van der Waals heterostructures when Cooper pairs from superconducting NbSe$_2$ tunnel through atomically thin magnetic insulator (MI) Cr$_2$Ge$_2$Te$_6$. Employing a superconducting quantum interference device based on MI JJs, we probe a doubly degenerate non-trivial JJ phase ($phi$) originating from the magnetic barrier. This $phi$-phase JJ is formed by momentum conserving tunneling of Ising Cooper pairs [5] across magnetic domains in the Cr$_2$Ge$_2$Te$_6$ barrier. The doubly degenerate ground states in MI JJs provide a two-level quantum system that can be utilized as a new disipationless component for superconducting quantum devices, including phase batteries [6], memories [7,8], and quantum Ratchets [9,10].