Using localization, we solve for the large-\(N\) master field of \(N=2^\ast\) super-Yang-Mills theory and calculate expectation values of large Wilson loops and the free energy. At weak coupling, these observables only receive non-perturbative contributions. The analytic solution holds for a finite range of the 't Hooft coupling and terminates at the point of a large-\(N\) phase transition. We find evidence that as the coupling is further increased the theory undergoes an infinite sequence of similar transitions that accumulate at infinity.