Resonant scattering, guided mode propagation phase, and/or orientation-dependent phase retardations are the three main mechanisms used to date to conceive optical metasurfaces. Here, we introduce an additional degree of freedom to address optical phase engineering by exploiting the topological features of non-Hermitian matrices operating near their singular points. Choosing metasurface building blocks to encircle a singularity following an arbitrarily closed trajectory in parameter space, we engineered a topologically protected full 2π-phase on a specific reflected polarization channel. The ease of implementation together with its compatibility with other phase-addressing mechanisms bring topological properties into the realm of industrial applications at optical frequencies and prove that metasurface technology represents a convenient test bench to study and validate topological photonic concepts.