  The physics of the Mott metal-insulator transition (MIT) has attracted huge
interest in the last decades. However, despite broad efforts, some key
theoretical predictions are still lacking experimental confirmation. In
particular, it is not clear whether the large coherent Fermi surface survives
in immediate proximity to the bandwidth-controlled first-order MIT. A
quantitative experimental verification of the predicted behavior of the
quasiparticle effective mass, renormalized by many-body interactions, is also
missing. Here we address these issues by employing organic $\kappa$-type salts
as exemplary quasi-two-dimensional bandwidth-controlled Mott insulators and
gaining direct access to their charge carrier properties via magnetic quantum
oscillations. We trace the evolution of the effective cyclotron mass as the
conduction bandwidth is tuned very close to the MIT by means of precisely
controlled external pressure. We find that the sensitivity of the mass
renormalization to tiny changes of the bandwidth is significantly stronger than
theoretically predicted and is even further enhanced upon entering the
transition region where the metallic and insulating phases coexist. On the
other hand, even at its very edge of stability the metallic ground state
preserves a large coherent Fermi surface with no significant enhancement of
scattering.
