Heat oil in a large stockpot or Dutch oven over medium-high heat.
Chop neck, heart, and gizzard into 2-inch pieces; add to pan.
Cook 5 minutes or until browned, stirring occasionally.
Add onion, celery, and carrot; cook 4 minutes or until tender, stirring frequently.
Stir in water and broth; bring to a boil.
Add thyme, peppercorns, parsley, and bay leaf.
Reduce heat and simmer 2 hours.
Strain mixture through a sieve over a large bowl; discard solids.
Cool discard fat.
Cover and chill overnight.
Skim the solidified fat from surface.