Drilling fluids and methods of making and using drilling fluids are provided. The drilling fluid includes an emulsion comprising an oleaginous phase suspended within an aqueous phase, a clay-based component in the aqueous phase, CaCl2, KCl, or both in the aqueous phase, and a polyglycerol-fatty acid complex. The polyglycerol-fatty acid complex may be free of covalent crosslinks. The polyglycerol-fatty acid complex may include polyglycerol hydrogen bonded to a fatty acid, and the oleaginous phase may include safra oil and the polyglycerol-fatty acid complex. Methods of producing the drilling fluid include reacting polyglycerol and a fatty acid at a temperature of less than 250° C. thereby forming a polyglycerol-fatty acid complex. The method further includes mixing an aqueous phase, a clay-based component, and the polyglycerol-fatty acid complex to produce a drilling fluid.