Two-dimensional (2D) gold nanoparticles can possess novel physical and chemical properties, which will greatly expand the utility of gold nanoparticles in a wide variety of applications ranging from catalysis to biomedicine. However, colloidal synthesis of such particles generally requires sophisticated synthetic techniques to carefully guide anisotropic growth. Here we report that 2D hyper-branched gold nanoparticles in the lateral size range of about 50 ~ 120 nm can be synthesized selectively on a 2D immiscible oil/water interface in a few minutes at room temperature without structure-directing agents. An oleic acid/water interface can provide diffusion-controlled growth conditions, leading to the structural evolution of a smaller gold nucleus to 2D nanodendrimer and nanourchin at the interface. Simulations based on the phase field crystal model match well with experimental observations on the 2D branching of the nucleus, which occurs at the early stage of growth. Branching results in higher surface area and stronger near-field enhancement of 2D gold nanoparticles. This interfacial synthesis can be scaled up by creating an emulsion and the recovery of oleic acid is also achievable by centrifugation.