Extra virgin olive oil (EVOO) is well known for containing relevant amounts of healthy phenolic compounds. The European Food Safety Authority (EFSA) allowed a health claim for labelling olive oils containing a minimum amount of hydroxytyrosol (OHTyr) and its derivatives, including tyrosol (Tyr). Therefore, harmonized and standardized analytical protocols are required in support of an effective application of the health claim. Acid hydrolysis performed after extraction and before chromatographic analysis has been shown to be a feasible approach. Nevertheless, other fast, green, and easy methods could be useful for on-site screening and monitoring applications. In the present research, a natural deep eutectic solvent (NADES) composed of lactic acid and glucose was used to perform a liquid/liquid extraction on EVOO samples, followed by UV-spectrophotometric analysis. The spectral features of the extracts were related with the content of total OHTyr and Tyr, determined by the acid hydrolysis method. The second derivative of spectra allowed focusing on three single wavelengths (i.e., 299 nm, 290 nm, and 282 nm) significantly related with total OHTyr, total Tyr, and their sum, respectively. In particular, the sum of OHTyr and Tyr could be determined with a root mean square error of prediction of 29.5 mg kg−1, while the limits of quantitation and detection were respectively 11.8 and 4.9 mg kg−1. The proposed method, therefore, represents an easy screening tool, with the use of a green, food-derived solvent, and could be considered as an attempt to pave the way for food grade analytical chemistry.