Consumer demand for plant-based meat alternatives and health concerns over animal fats have propelled the exploration of edible oil structuring techniques, for mimicking animal fat texture and functionality. In this context, the use of food polymers offers possibilities in conferring viscoelastic properties to oil structured in heterogeneous systems. Many reported examples were predominantly structured by proteins, however, which are sensitive to ionic strength. In this work, we offer an alternative approach through emulsion gel structuring using curdlan and citrus fibre, which are natural and more process-stable food polymers. This work reports insights gained on emulsion gel strengthening with the use of laccase-oxidised phenolic compounds. Our key results reveal the use of laccase-oxidised ferulic acid at millimolar concentration against 10% (w/w) curdlan to be particularly promising, in that (i) it strengthened inter-triplex network in heat-set curdlan, as supported by the increase in glass transition temperature of curdlan; (ii) it generated quinones as determined by nitro blue tetrazolium-glycinate assay, which could crosslink interfacial fibre having trace nitrogen; and (iii) consequently, the emulsion gel system became stronger against high strain compression. Crosslinking at inter-oil-droplet bridges with well-controlled oil aggregate sizes was pivotal, and this could be optimised with suitable sequencing of formulation steps that keep the aqueous phase viscosity low during emulsification. Overall, our findings provide reference value in the creation of stiff animal fat mimetics out of unsaturated edible oils.