Combine first 3 ingredients in an 8-quart stockpot. Bring to a boil over medium-high heat. Reduce heat to low, and simmer 2 hours and 45 minutes, skimming off and discarding foam as needed. Strain stock through a fine sieve into a large bowl; discard solids.
Combine 1 tablespoon water and saffron in a small bowl, stirring with a whisk. Stir saffron mixture into stock. Cool stock to room temperature; cover and refrigerate 5 hours or overnight. Skim solidified fat from surface; discard fat.
