The food industry is focused on developing plant-based foods that incorporate pea protein isolates. However, these ingredients are often described as having persistent beany, bitter, and astringent notes, which can decrease the desirability of the resulting foods. These perceptions are rooted in the complex composition of volatile and non-volatile compounds in foods. The aim of our study was to better understand how the volatile and non-volatile fractions of pea protein isolates influence the perception of pea-protein-based foods. To this end, a mixture design was used. First, we obtained three fractions (the pellet, permeate, and retentate) from two pea protein isolates, resulting in a total of six fractions. Second, we used various combinations of the six fractions to create a set of 46 pea-protein-based solutions via various processes (solubilization, centrifugation, filtration, and mixing). Each fraction was specifically representative of the following constituent groups: insoluble proteins (the pellet); soluble compounds, such as volatiles, peptides, and phenolics (the permeate); and soluble proteins interacting with volatiles (the retentate). Factor levels were chosen with two aims: to explore the widest possible range of combinations and to realistically represent protein concentrations so as to build optimal mixture models. Third, 17 trained panelists were asked to score the attributes of the solutions using sensory profiling. Model performance was assessed using analysis of variance; results were significant for 18/18 attributes, and there was no significant lack-of-fit for 17/18 attributes. It was also assessed using the results of trials conducted with six supplementary solutions. These results clarified the origin of the perceived beany, bitter, and astringent notes. Beaniness was mainly influenced by the retentate and permeate fractions and was strongly affected by hexanal levels. Bitterness was mainly influenced by the retentate fraction, whereas astringency was influenced by the retentate and pellet fractions. Additionally, perception of these latter two attributes was affected by caffeic acid levels. This study has increased understanding of the relationship between pea protein fractions and the undesirable sensory attributes of pea protein isolates. It has also revealed how fraction-based formulation could be used to reduce the beaniness, bitterness, and astringency of pea-protein-based foods.