The liquid-liquid phase separation of a binary solvent can be arrested by colloidal particles trapped at the interface [K. Stratford, Science 309, 2198 (2005)]. We show experimentally that the colloidal network so formed can remain stable after fully remixing the liquids, creating a new type of gel in which colloids in a single-phase solvent have locally planar coordination. We argue that this structure is likely maintained by primary-minimum Derjaguin-Landau-Verweg-Overbeek bonding of our charged colloids, created under strong compression by capillary forces. We present simulation evidence that the combination of a short-ranged attraction with a repulsive barrier can strongly stabilize such locally planar gels.