In this study, vortex-assisted liquid-liquid microextraction (VA-LLME) based on hydrophobic deep eutectic solvents (HDES) was used to efficiently and sustainably extract five phenolic acids and tetramethylpyrazine (TMP) from Shanxi aged vinegar (SAV). The VA-LLME technique was employed to investigate the extraction mechanism of HDES with the best extraction performance for the target compounds using a conductor-like screening model for real solvents (COSMO-RS). An artificial neural network combined with a genetic algorithm (ANN-GA) was developed to optimize the extraction conditions based on single-factor and response surface methodology, while also analyzing the interactive effects on the phenolic acids and TMP in the extracted solution during the extraction phase. The optimized conditions were determined, and the greenness of the procedure was evaluated using an analytical greenness metric, indicating that this technique can serve as a green alternative for the determination of phenolic acids and TMP in SAV.