Electronic waste grows globally at a rate of 5% annually, which makes electronic waste recycling (WEEE recycling) an urgent task aimed at achieving (i) environmental protection and (ii) the preservation of mineral resources through the re-introduction of strategic metals into the market. As it turns out, WEEE recycling produces further waste, called WEEE secondary waste, which still contains valuable metals such as gold, silver, and copper. This study assessed the economic viability of recovering these metals and identified the most promising targets and approaches. WEEE secondary waste produced at a plant in southern Europe was sampled and examined for this purpose. The study methods included an ANOVA (analysis of variance) and an OCCP (orthogonal central composition plan). Over 90% gold, silver, and copper extraction was achieved with hydrochloric acid leaching in sodium hypochlorite with sodium chlorite as an oxidizing agent at 60 °C. The significance of the variation in the response for each factor, calculated using the Yates algorithm, demonstrates that by excluding sodium chloride and optimizing the doses of hydrochloric acid and sodium hypochlorite, gold can be selectively recovered through the leaching process. The scenario of HCl (2.5M)/NaClO (5%) leaching results in the maximum extraction effect of Au (91.6%) at the lowest concentrations of Ag and Cu (37–44%).