A series of laboratory experiments was conducted to study the flows and exchange processes generated by turbulent convection in a shallow fluid with a combination of a shelf and slope topography in the presence of rotation. For convenience, heat loss at the ocean surface was modelled by heating from below with a buoyancy flux B0 applied to a circular portion (of radius R) of the base of a cylindrical tank, rotating with angular frequency f. The working volume was closed by an inverted model of a shelf and slope topography (with slope angle ϕ), creating a fluid height H between the forced surface and the shelf. After the initiation of the buoyancy forcing, the average temperature in the actively convecting region initially increases linearly with time but slows down once a lateral heat flux is generated by baroclinic instability at the edge of the convecting region. The wavelength of this instability is described by λ=(5.9±0.3) RD, with RD the Rossby radius of deformation, defined by (g′H)1/2/f, where g′ is the reduced gravity based on the density difference between the convecting and ambient fluids. A steady state is eventually reached when the lateral heat flux balances the (vertical) heat flux due to the forcing. The results differ from previous work in either unbounded or in constant-depth environments. It is shown that the steady-state density anomaly between the convecting and ambient regions is given by g′f=(1.6±0.2) (B0f)1/2 (R/H), while the time to reach this steady state is τ=(3.1±0.5) (f/B0)1/2R. The eddy velocity, characterizing the lateral exchange process, is given by vflux≈1.2 (B0/f)1/2. These results are consistent with the description of the lateral exchange process by eddy diffusion (rather than advection). Comparisons are made between the experimental results and field observations of convection events.