The widespread prevalence of commercial products made from microgels illustrates the immense practical value of harnessing the jamming transition; there are countless ways to use soft, solid materials that fluidize and become solid again with small variations in applied stress. The traditional routes of microgel synthesis produce materials that predominantly swell in aqueous solvents or, less often, in aggressive organic solvents, constraining ways that these exceptionally useful materials can be used. For example, aqueous microgels have been used as the foundation of three-dimensional (3D) bioprinting applications, yet the incompatibility of available microgels with nonpolar liquids, such as oils, limits their use in 3D printing with oil-based materials, such as silicone. We present a method to make micro-organogels swollen in mineral oil, using block copolymer self-assembly. The rheological properties of this micro-organogel material can be tuned, leveraging the jamming transition to facilitate its use in 3D printing of silicone structures. We find that the minimum printed feature size can be controlled by the yield stress of the micro-organogel medium, enabling the fabrication of numerous complex silicone structures, including branched perfusable networks and functional fluid pumps.