To meet the growing demand for high-quality extra-virgin olive oil (EVOO) with health-promoting properties and pleasant sensory properties, studies are needed to establish optimal production parameters. Bioactive components of EVOO, including phenolic compounds, carotenoids, chlorophylls, tocopherols, and squalene, contribute to its organoleptic properties and beneficial health effects. The aim of this study was to develop an Arbequina EVOO with high phenol content, particularly oleocanthal and oleacein, on a laboratory scale by analyzing the effects of different temperatures (20, 25, and 30 °C) and times (30 and 45 min) of malaxation. Higher temperatures decreased the levels of the phenolic compounds, secoiridoids, tocopherols, and squalene, but increased the pigments. EVOO with the highest quality was produced using malaxation parameters of 20 °C and 30 min, although oleocanthal and oleacein were higher at 30 and 25 °C, respectively. Overall, 20 °C and 30 min were the processing conditions that most favored the physiological and chemical processes that contribute to higher levels of bioactive compounds in the oil and diminished their degradation and oxidation processes.