The Annurca type is an historical Italian apple fruit probably native to the Campania region. These fruits are harvested before a full maturity stage and go through an open-field reddening process. Products based on 1-methylcyclopropene (1-MCP) are widely used in postharvest to improve apple quality and avoid disorders in controlled atmosphere. In this work, we tested the impact of 1-MCP in the traditional reddening system of Annurca type by analyzing three postharvest strategies, namely, fruits exposed for ten days to the traditional reddening and then cold-stored (RDG treatment); fruits treated in postharvest with 1-MCP and then cold-stored (MCP treatment); fruits treated in postharvest with 1-MCP, exposed for ten days to the open-field reddening and then cold-stored (MCP + RDG treatment). Using a full factorial design, we measured main physical and compositional traits and described the properties of the products by consumer testing at two storage times. The MCP + RDG treatment provided the most valuable results, by positively affecting fruit flesh firmness and several sensorial attributes (e.g., hardness, crunchiness, juiciness, sweetness), including a reduction of the mealiness. At the end of the cold-storage, MCP + RDG apples scored a higher consumer’s overall liking. The work demonstrated that the 1-MCP technology can be integrated into a traditional open-field postharvest process to improve fruit quality and, potentially, to extend the shelf life of Annurca apples.