At a time when museumgoing is increasingly homogenized and the world’s large, prestigious fine-arts institutions often offer what feel like prepackaged experiences, Parma’s 500,000-square-foot Palazzo della Pilotta offers something different, with a strong sense of local identity, soulfulness, even eccentricity.

This begins with physical scars on the façade that testify to an Allied bombing raid in World War II. The battered structures that make up the museum are asymmetrical and, despite their monumental size, elusive. As you approach the complex, the entrance is tucked into an opening on the left—but there are so few visitors you can miss it.