In this work, a green and practical analytical method based on natural deep eutectic solvents (NADES) as extraction agents and nano-liquid chromatography as a separation technique was developed. To demonstrate the applicability of the methodology, alkylphenols and bisphenol A were evaluated as model compounds in olive and sunflower oils as model fatty samples by liquid–liquid microextraction. With this aim, several NADES based on mixtures of choline chloride with glycerol, lactic, ascorbic, and citric acids or glycerol with amino acids were evaluated as potential extraction solvents. In addition, to select the most suitable stationary phase for the separation of this group of contaminants, some stationary phases were tested, including Pinnacle II phenyl, Cogent Bidentate C18™, and XBridge® C18. The last one provided the best performance with an analysis time of 11 min. To solve the problem of the compatibility of hydrophilic NADES with chromatographic systems without harming the solubility of analytes, different aqueous organic mixtures were tested. Methanol/water mixtures were the most suitable as an injection solvent. Finally, following the White Analytical Chemistry principles, different tools were used to evaluate the greenness, the practicality, and applicability of the method based on the Analytical Eco-Scale, the Analytical GREEnness metric approach, and the Blue Applicability Grade Index.