The purpose of this study is to develop nut and legume flour-based cookie formulations with improved functional properties and to investigate the rheological, spectroscopic, and technological characteristics of these products. In addition to sensory testing, the rheological, spectroscopic, and technological properties of cookies made with different ratios of double (combinations of chickpea-hazelnut and chickpea-carob flours) and triple composite flours (chickpea-hazelnut-carob flours) were assessed. The findings of the flour analyses show that the protein contents of raw and cooked chickpea flours are higher than wheat flour. Hazelnut flour stands out for having a high-fat content; 35 times higher compared to wheat flour, and 6 times as chickpea flour. Pre-cooked chickpea flour has a strong capacity to retain water when compared to the other flours used in the formulation of gluten-free cookies. Its capacity to hold water is about 3.5 times greater than that of wheat flour. The sample with 90% chickpea flour has the highest firmness (N) value and the greatest difference from the other formulations, according to the rheological properties. However, among all the samples, the dough with the highest hazelnut content (60%) gets the lowest firmness grade. In accordance with principal component analysis, all cookie dough samples that contain double and triple composite flours are grouped based on their formulations, and cookies that just contain chickpea flour are separated from the others. Moreover, it may be concluded from the sensory evaluation of the cookies that the inclusion of hazelnut and carob flour influences customer preferences favorably.