Plant-based oil inks that imitate the texture and melting behavior of traditional animal fats using 3D printing have been developed. The influence of the incorporation of potato starch and the type of oil on rheology and meltability was investigated. The results showed that the dynamic modulus and hardness of fat analogs increased, whereas fat analog meltability decreased with an increase in potato starch content. Coconut oil and soybean oil-containing fat analogs incorporated with proper potato starch levels exhibited good printability and similar meltability to commercial beef and pork fats. The addition of potato starch suppressed fat analog meltability as it disrupted the inulin matrix. Fat analogs containing coconut oil could be texturized at temperatures lower than those required for their soybean oil counterparts. The fat analogs were solid at room temperature, demonstrated good printability, and imitated the melting behavior of fat contained in real meat throughout the cooking process.