Sulforaphane (SFN) is a powerful health-promoting compound found in broccoli in the form of its inactive precursor, glucoraphanin (GFN). SFN formation occurs through the enzymatic hydrolysis of glucoraphanin by myrosinase under specific chemical conditions. Its incorporation in food formulations has been hindered by the thermal instability of SFN and low concentration in Brassicaceae. Then, extracting SFN from broccoli at a temperature below 40 °C appears as an option to recover and stabilize SFN, aiming at delivering it as a nutraceutical. We studied an eco-friendly extraction process to obtain an SFN-rich extract from broccoli. The effect of the broccoli mass/solvent ratio, ethanol concentration in the extractant solution, and extraction time on the recovery of SFN, GFN, phenolic compounds, and antioxidant activity were studied through a Box–Behnken design. The regression models explained more than 70% of the variability in the responses, adequately representing the system. The experimental factors differently affected the bioactive compound recovery and antioxidant activity of the extracts. The extraction conditions that allowed the highest recovery of bioactive compounds and antioxidant activity were identified and experimentally validated. The results may provide the basis for the design of a process to produce a sulforaphane-rich food supplement or nutraceutical by using a GRAS extractant.