  The correlation-driven Mott transition is commonly characterized by a drop in
resistivity across the insulator-metal phase boundary; yet, the complex
permittivity provides a deeper insight into the microscopic nature. We
investigate the frequency- and temperature-dependent dielectric response of the
Mott insulator $\kappa$-(BEDT-TTF)$_{2}$-Cu$_2$(CN)$_3$ when tuning from a
quantum spin liquid into the Fermi-liquid state by applying external pressure
and chemical substitution of the donor molecules. At low temperatures the
coexistence region at the first-order transition leads to a strong enhancement
of the quasi-static dielectric constant $\epsilon_1$ when the effective
correlations are tuned through the critical value. Several dynamical regimes
are identified around the Mott point and vividly mapped through pronounced
permittivity crossovers. All experimental trends are captured by dynamical
mean-field theory of the single-band Hubbard model supplemented by percolation
theory.
