In recent years, the consumption of gluten-free products has increased due to the increasing prevalence of celiac disease and the increased preference for gluten-free diets. This study aimed to make cookies using a mixture of cañihua flour, whey, and potato starch. The use of a Box–Behnken design allowed for flexible ingredient proportions and physicochemical properties, centesimal com position, color, texture, and sensory attributes to be evaluated through consumer tests (Sorting and acceptability). The results highlighted significant variations in physicochemical data, composition, color, and texture across formulations. The blend with 38.51% cañihua flour, 10.91% sweet whey, 25.69% potato starch, 8.34% margarine, 11.10% sugar, 0.19% sodium chloride, 0.51% baking powder, 0.51% vanilla essence, and 4.24% egg exhibited superior sensory appeal. This formulation boasted excellent texture, aroma, flavor, color, and appearance, indicating high sensory and physicochemical quality. The use of cañihua flour, sweet whey, and potato starch not only provides a gluten-free option but also delivers a nutritious and sensorily pleasing choice for those with dietary restrictions. Future research could explore the commercial viability of producing these cookies on a larger scale, as well as investigating the potential health benefits of these ingredients.