Recent experiments have demonstrated magnetic reconnection between colliding plasma plumes, where the reconnecting magnetic fields were self-generated in the plasma by the Biermann battery effect. Using fully kinetic 3-D simulations, we show the full evolution of the magnetic fields and plasma in these experiments including self-consistent magnetic field generation about the expanding plume. The collision of the two plasmas drives the formation of a current sheet, where reconnection occurs in a strongly time-and space-dependent manner, demonstrating a new 3-D reconnection mechanism. Specifically, we observe fast, vertically-localized Biermann-mediated reconnection, an inherently 3-D process where the temperature profile in the current sheet coupled with the out-of-plane ablation density profile conspires to break inflowing field lines, reconnecting the field downstream. Fast reconnection is sustained by both the Biermann effect and the traceless electron pressure tensor, where the development of plasmoids appears to modulate the contribution of the latter. We present a simple and general formulation to consider the relevance of Biermann-mediated reconnection in general astrophysical scenarios.