Heat oil in a large stockpot over medium-high heat. Add heart, neck, and gizzard; sauté 5 minutes. Add onion, carrot, and celery; sauté 4 minutes. Add water and broth; bring to a boil. Add thyme, peppercorns, parsley, and bay leaf. Reduce heat; simmer 2 hours. Strain through a sieve over a bowl; discard solids. Cool to room temperature. Cover and chill overnight. Skim solidified fat from surface.