Traveling to learn about the gastronomy of a destination is becoming increasingly important among tourists, especially in the wake of the pandemic. Quality foods endorsed by protected designations of origin (PDOs) are increasingly in demand, as are experiences related to their production processes. In this study, the seven PDOs in the province of Córdoba (Spain) are analyzed. These PDOs produce olive oil, wine or ham. A field study was performed, whereby 315 gastronomic tourists who visited a gastronomic route or a PDO in Córdoba were surveyed. The objective was to characterize the profile of visiting tourists and to anticipate future demand using ARIMA models. The results indicate that the growth in gastronomic tourism in Córdoba is lower than that in the wider region, and that there are no significant differences among the different profiles (oil tourist, enotourist and ham tourists) due in part to the fact that most tourists travel from nearby regions. The novelty of this study is that three products are analyzed, and strategies are proposed to deseasonalize this type of tourism, for example, by creating a gastronomic brand that represents Córdoba and selling products under that brand (especially in international markets), by highlighting raw materials and prepared dishes and by making gastronomy a complement to heritage tourism in the city and rural tourism in the province.