A method for making natural oil-based polyols directly from vegetable or animal oil using a consecutive two-step process involving epoxidation and hydroxylation is provided. Specifically, this process comprises adding a peroxyacid to a natural oil wherein said natural oil and said peroxyacid react to form an epoxidized natural oil and adding said epoxidized natural oil to a mixture of an alcohol, water, and a fluoboric acid catalyst. The catalytic amount of fluoboric acid is less than about 0.5% by weight of the entire reaction mixture, and the amount of water is about 10 to 30% by weight of the entire mixture. The epoxidized natural oil undergoes hydroxylation and forms a natural oil-based polyol. The present invention further includes a method for making natural oil-based polyols from epoxidized oil by hydroylating the epoxidized oil in the presence of fluoboric acid, alcohol and water in the amounts discussed above. The natural oil-based polyols created by this method may be reacted with isocyanates so as to form polyurethanes, which is another embodiment of the present invention. Alternatively, fillers such as silica may be combined with these natural oil-based polyols before they are reacted with isocyanates to form polyurethanes. In still another embodiment of the present invention, polyurethanes made from natural oil-based polyols may be used to form electroinsulating casting resins for use in electrical applications.