The olive oil sector is continuously evolving in order to improve the quality of olive oil and its by-products. In fact, the trend is to use increasingly greener olives to improve quality by decreasing the extraction yield, thus obtaining a higher content of antioxidant phenolics. The application of a cold-pressing system to the olive before the extraction of oil was tested with three varieties: picual at three different stages of maturity and arbequina and hojiblanca at early stages of maturity. The Abencor system was used for the extraction of virgin olive oil and its by-products. For the quantification of phenols and total sugars for all phases, organic solvent extractions and colorimetric measurements and high-performance liquid chromatography (HPLC) with a UV detector were used. The results show that the new treatment significantly improved the amount of oil extracted by between 1 and 2% and even increased its concentration of total phenols by up to 33%. Regarding the by-products, the concentrations of the main phenols, such as hydroxytyrosol, increased by almost 50%, as did the glycoside. The treatment also facilitated the separation of phases in by-products and improved the phenolic profile, although not in terms of total phenols, but individual phenols with higher antioxidant activity were obtained.