Given the substantial variation in global wheat yield, insufficient research in cultivar selection for climate change, and the lack of suitable germplasm in sustainable agroecosystems, there is a requisite for soft wheat genotypes, with stable grain yield as well as quality parameters. The present study was aimed at genotype evaluation (GGE biplot for “mean performance versus stability”) not only for yield, but also for technological, phytosanitary and functional quality parameters of 24 Triticum aestivum L. genotypes (eight landraces, old and modern varieties, respectively) within a single organic farm location (Argelato, Emilia-Romagna, Italy) over three consecutive years. Overall, high yield stability was shown for the landraces and old varieties. In particular, the landraces Piave and Gamba di Ferro, as well as the old variety Verna, showed high stability with above-average means for numerous quality parameters of interest. Additionally, relative stability combined with above-average mean for quality parameters was also demonstrated for the high-yielding Gentil Bianco and Guà 113. Aside from Verna, these “unrecognized” resilient genotypes were also shown to meet the requisites for suitable germplasm in sustainable agroecosystems. Future potential utilization of these more stable landraces in addressing climate change would also ultimately facilitate the survival of valuable genetic resources.