Tailored foods are specifically suitable for target groups of people with particular nutritional needs. Although most research on tailored foods has been focused on increasing the nutrient content in plant tissues (biofortification), in populations with specific physiological conditions, it is recommended to reduce the uptake of specific nutrients in order to improve their health. People affected by chronic kidney disease (CKD) must limit their consumption of vegetables because of the generally high potassium (K) content in the edible parts. This study aimed to define an appropriate production technique for two baby leaf vegetables, spinach (Spinacia oleracea L.) and Swiss chard (Beta vulgaris L. ssp. vulgaris), with reduced K tissue content, minimizing the negative effects on their crop performance and overall nutritional quality. Plants were grown in a hydroponic floating system. The K concentration in the nutrient solution (NS) was reduced from 200 mg/L (K200, the concentration usually used for growing baby leaf vegetables in hydroponic conditions) to 50 mg/L over the entire growing cycle (K50) or only during the seven days before harvest (K50-7d). The reduction of K in the NS resulted in a significant decrease of K tissue content in both species (32% for K50 and 10% for K50-7d, on average), while it did not, in general, compromise the crop performance and quality traits or the bioaccessibility of K, magnesium, and calcium. The production of reduced-potassium leafy vegetables is a feasible tailored nutrition approach for CKD patients in order to take advantage of the positive effects of vegetable consumption on health without excessively increasing potassium intake.