The scarcity of geochemical constraints on the Hadean climate limits our understanding of the planetary environment that gave rise to life on the earliest Earth. I will describe how rocky exoplanets open a novel observational window into the geodynamic evolution of terrestrial worlds that is unavailable in the Solar System. Some of these planets orbit so closely to their star that they lack an atmosphere, which gives direct access to their surfaces. Geodynamic simulations of the super-Earths LHS 3844b and GJ 486b suggest that solid but tidally-locked rocky exoplanets undergo a hemispherically-forced tectonic regime, unknown in the Solar System, with volcanic activity focused either on the day- or nightside, potentially driving asymmetric outgassing. The dense sub-Earth GJ 367b, on the other hand, likely hosts a day-side magma ocean, enabling inferences on accretion regime and the evolution of melting geometry and surface composition over geologic time. Scheduled high-resolution observations with JWST of these and similar exoplanets will enable novel tests of fundamental models of planetary geodynamics, atmospheric formation, and planetary accretion.