The growing interest in plant protein sources, such as pulses, is driven by the necessity for sustainable food production and climate change mitigation strategies. Faba bean (Vicia faba L.) is a promising protein crop for temperate climates, owing to its remarkable yield potential (up to 8 tonnes ha−1 in favourable growing conditions) and high protein content (~29% dry matter basis). Nevertheless, the adoption of faba bean protein in plant-based products that aim to resemble animal-derived counterparts is hindered by its distinctive taste and aroma, regarded as “off-flavors”. In this review, we propose to introduce off-flavor as a trait in breeding programs by identifying molecules involved in sensory perception and defining key breeding targets. We discuss the role of lipid oxidation in producing volatile and non-volatile compounds responsible for the beany aroma and bitter taste, respectively. We further investigate the contribution of saponin, tannin, and other polyphenols to bitterness and astringency. To develop faba bean varieties with diminished off-flavors, we suggest targeting genes to reduce lipid oxidation, such as lipoxygenases (lox) and fatty acid desaturases (fad), and genes involved in phenylpropanoid and saponin biosynthesis, such as zero-tannin (zt), chalcone isomerase (chi), chalcone synthase (chs), β-amyrin (bas1). Additionally, we address potential challenges, including the need for high-throughput phenotyping and possible limitations that could arise during the genetic improvement process. The breeding approach can facilitate the use of faba bean protein in plant-based food such as meat and dairy analogues more extensively, fostering a transition toward more sustainable and climate-resilient diets.