Sweet basil (Ocimum basilicum L.) is an economically important leafy vegetable especially in Mediterranean countries. In Italian gastronomy, the large elliptical leaves of the Genovese type are mostly used for the well-known pesto sauce, and almost all (>90%) professional production is for the food industry. The growing demand for fresh leaves with standardized technological and sensory characteristics has prompted basil producers to adopt advanced cultivation methods such as the floating raft system (FRS). The aim of this study was to evaluate the productive, qualitative, and physiological performance of three Genovese basil cultivars (“Aroma 2,” “Eleonora,” and “Italiano Classico”) in two successive harvests and at two densities (159 and 317 plants m–2). Caffeic, chicoric, rosmarinic, and ferulic acid were determined through the high-performance liquid chromatography (HPLC) system, whereas the extraction and quantification of the volatile organic compounds (VOCs) were performed by solid-phase microextraction (SPME) and gas chromatography coupled to a mass spectrometer (GC/MS). “Aroma 2” showed the highest fresh yield and photosynthetic rate together with the lowest nitrate content. For all the tested cultivars, the higher density, while reducing the number of leaves per plant, resulted in higher fresh and dry production per unit area, without altering the aroma profile. Successive harvests resulted in a significant increase in both the yield (37.5%) and the total phenolic acids (75.1%) and favored Eucalyptol and 1-octen-3-ol accumulation (+25.9 and +15.1%, respectively). The here presented comprehensive and multifactorial assessment of the productive and qualitative response of basil provides evidence of the positive effects (from biomass to specialized metabolites) that can be obtained from the management of the pre-harvest factors in soilless cultivation. In addition, it also highlights the role and constraints of the genetic factor in the observed response. We also discuss the implications of our work considering the impact for the food processing industry. Future research may explore the phenolic acids accumulation as a possible fortification means to extend the pesto sauce shelf life, reducing the need of added antioxidants and thermal processing.