The oxidative stability of extra virgin olive oil (EVOO) depends on its composition, primarily, phenolic compounds and tocopherols, which are strong antioxidants, but also carotenoids, squalene, and fatty acids contribute. The aim of this study was to evaluate the effect of malaxation conditions and olive storage on the composition of ‘Corbella’ EVOO produced in an industrial mill to determine which parameters and compounds could give more stable oils. Although a longer malaxation time at a higher temperature and olive storage had a negative effect on the content of α-tocopherol, squalene, flavonoids, lignans, phenolic acids, and phenolic alcohols, the antioxidant capacity and oxidative stability of the oil were improved because of an increase in the concentration of oleacein (56–71%) and oleocanthal (42–67%). Therefore, these two secoiridoids could be crucial for better stability and a longer shelf life of EVOOs, and their enhancement should be promoted. A synergistic effect between secoiridoids and carotenoids could also contribute to EVOO stability. Additionally, ‘Corbella’ cultivar seems to be a promising candidate for the production of EVOOs with a high oleic/linoleic ratio. These findings signify a notable advancement and hold substantial utility and significance in addressing and enhancing EVOO stability.