The potentiality of a multidimensional comprehensive gas chromatographic (GC × GC) method, employing a simultaneous dual detection (FID and mass spectrometer), to generate peculiar two-dimensional chromatograms to be used as a chemical fingerprint, was investigated to characterize minor compounds in edible oil, particularly olive oil. The best column combination for this application was investigated comparing two column sets (orthogonal or reverse-type), equivalent in terms of theoretical plate number, but differing in stationary phase combination. The apolar × mid-polar set gave a superior separation power, thus was used for further characterization. Different levels of information were extrapolated from the two-dimensional chromatogram. Using the FID, reliable quantification of the alkyl esters fatty acids and waxes was obtained, comparable to the results obtained using the official method, as required by the European legislation. However, thanks to a slight modification of the sample preparation method, the increased separation power obtained using the GC × GC method, and the support of the mass spectrometer detector, further diagnostic information was extrapolated considering the free sterol and tocopherol fractions. In particular, the profiles of extra virgin olive oil samples were compared with a hazelnut oil sample, highlighting that the latter was characterized by a larger number of compounds, completely absent in the extra virgin olive oil samples, which can be used to detect illegal admixtures.