Vegetables of the plant order Brassicales are believed to have health-promoting properties, as they provide high contents of glucosinolates (GLS) and deriving from these, enzymatically and heat-induced breakdown products, such as isothiocyanates (ITC). Besides their positive physiological effects, ITC are electrophilic and can undergo reactions with food components such as proteins. Following the trend of improving traditional food products with GLS-rich ingredients, interactions of ITC with proteins can diminish the properties of both components—protein’s value and functionality as well as ITC’s bioactivity. In vegetable-enriched bread, where cresses (Lepidium sativum L. or Tropaeolum majus L.) are added to the initial dough, together with benzyl cyanide, benzyl isothiocyanate (BITC) is formed during the baking process. The aim of the present study was to investigate the possible migration behavior of the GLS breakdown products and the formation of ITC-wheat protein conjugates. After the baking process, the breads’ proteins were enzymatically hydrolyzed, and the ITC-amino acid conjugates analyzed using a LC-ESI-MS/MS methodology. In all samples, BITC-protein conjugates were detected as thiourea derivatives, while formation of dithiocarbamates could not be detected. The study showed that GLS and their breakdown products such as ITC migrate into the surrounding food matrix and undergo reactions with proteins, which could in turn lead to modified protein properties and reduce the bioavailability of ITC and lysine.