Cadherins mediate cell-cell adhesion and help the cell determine its shape and function. Here we study collective cadherin organization and interactions within cell-cell contact areas, and find the cadherin density at which a 'gas-liquid' phase transition occurs, when cadherin monomers begin to aggregate into dense clusters. We use a 2D lattice model of a cell-cell contact area, and coarse-grain to the continuous number density of cadherin to map the model onto the Cahn-Hilliard coarsening theory. This predicts the density required for nucleation, the characteristic length scale of the process, and the number density of clusters. The analytical predictions of the model are in good agreement with experimental observations of cadherin clustering in epithelial tissues.