From a circular bio-economy perspective, biomass valorization requires the implementation of increasingly efficient extraction techniques to ensure the environmental and economic sustainability of biorefining processes. This research focuses on optimizing the specialized metabolite extraction of Turkey oak chips from Quercus cerris L. by applying a 3 levels Full Factorial Design (FFD). The goal is to obtain an extract with the highest antioxidant activity [evaluated by 1,1-diphenyl-2-picryl hydrazyl (DPPH) scavenging activity and ferric reducing antioxidant power (FRAP) assays] and specialized metabolites content [measured as total phenolic content (TPC), total flavonoid content (TFC), condensed tannin content (CTC), and hydrolysable tannins content (THC)]. With this objective, three different variables were investigated and compared: temperature (20 °C, 50 °C, 80 °C), solvents EtOH/H2O (0%, 20%, 40%), and time (3 h, 6 h, 24 h), resulting in 27 different extracts. Following the FFD analysis, the optimal extractive conditions were determined to be 80 °C, 40% EtOH/H2O, and 19.8 h. Finally, the prediction ability of FFD was compared with that of artificial neural network (ANN) for DPPH scavenging activity, FRAP, and TPC data based on the coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE). The results indicated that ANN predictions were more precise than FFD ones; however, both methods were useful in optimizing the extraction process as they returned comparable optimized extraction parameters.