The onion is one of the most cultivated and consumed vegetables, and is a very valuable source of antioxidant substances. Every onion variety is rich in flavonols—mainly quercetin derivatives which makes onions the main dietary source of these compounds. This study intends to develop an ultrasound-assisted extraction method (UAE), an economical, green, and efficient technique, that allows us to determine the quality of onion extracts in terms of flavonol composition and antioxidant activity. For this purpose, an ultrasound-assisted extraction method has been optimized to obtain extracts with a high amount of flavonols, as well as with a high antioxidant activity, not only separately using a Box–Behnken design, but also simultaneously, based on multi-response optimization. Multiple response optimization has not only demonstrated an efficacy level similar to that of the individual ones, but it also represents a considerable reduction in terms of cost, time and work. The optimal conditions for simultaneous extractions were determined as follows: 76.8% methanol as an extraction solvent at pH 2 and 58.5 °C temperature, 85% amplitude, 0.9 s cycle, and 0.2:13 g:mL sample mass/solvent volume ratio. Furthermore, the developed method exhibited a high precision level and great recoveries in a rather short extraction time (2 min). These results, together with the development of a fast and simple UHPLC analysis method, lead us to consider the developed UAE method as a suitable technique for the extraction of bioactive compounds from onion matrices.