In order to contribute to the reduction of nutritional deficiencies in Morocco, this study was undertaken to develop a healthier tortilla with higher iron and protein, while maintaining adequate technological and sensory qualities. Composite durum wheat flour enriched with 20, 25, 30, and 35% chickpea flour was assessed for nutritional, functional, and technological properties. Then, we selected two composite blends of 75:25 and 70:30 of durum wheat and chickpea flours for making tortillas to study nutritional, technological, and sensorial qualities. In addition, we studied the effects of making and cooking process and storage time. Kruskal–Wallis and Mann—Whitney tests were used for data analysis, and GraphPad Prism was used to create graphs. The results showed that composite tortilla had significantly higher nutritional value than durum wheat tortilla, and the best ratio was 30% chickpea flour. At this ratio, the results showed the best cooking time and the best yellowness, but tortilla fluffiness and puffiness decreased. Tortilla processing significantly increased protein at 30% chickpea flour, while minerals except sodium, weight, and diameter decreased. Adding 30% chickpea flour to durum wheat tortilla improved flavor. Then, storage decreased the weight resulting in decreased flexibility, and sanitary quality was lost early for 30% chickpea flour. In conclusion, adding 30% chickpea flour to durum wheat flour results in a healthier and tastier tortilla, which should be consumed fresh.