Place prosciutto in a large pot with 12 cups water; bring to a boil over medium heat. Reduce heat to medium-low and simmer, skimming surface occasionally, until the fat from the prosciutto is rendered into the broth, about 2 hours.
Strain through a fine-mesh strainer into an airtight container; let cool. Cover and keep refrigerated for up to 1 week, or freeze for up to 3 months. Before using, bring broth to a simmer and stir to reincorporate fat.