For the stock: Preheat the oven to 450 degrees F.
Place the chicken wings in a roasting pan or large ovenproof skillet. Add the oil and toss to coat. Place the wings in the oven and cook until fully browned, 20 to 25 minutes.
Remove the pan from the oven. Transfer the wings to a pressure cooker and drain off a little fat. (Reserve it for another use.) Place the pan on the stovetop over medium heat and add the celery, onions, carrots, garlic and herbs. Using a wooden spoon, stir the mixture until it starts to brown and is lightly caramelized, 10 to 12 minutes. Once caramelized, add 1/2 cup water to the pan and use the wooden spoon to scrape up all the browned bits. Transfer the entire mixture to the pressure cooker. Add 5 1/2 cups water and the soy sauce and bring to a boil. Place the top securely on and let it cook at full steam for 35 to 40 minutes. Remove the lid from the pressure cooker once all of the steam has released. Let the stock cool completely. (Store it in the refrigerator if making ahead of time.) Skim the fat off the top and discard. Strain the stock and discard the solids.
For the gravy: Ladle about 1 cup stock into a medium-size mixing bowl. Add the cornstarch and whisk together until smooth to make a slurry. Then whisk the slurry back into the stock. Add the turkey heart and gizzard. Using an immersion or regular blender, process the mixture until completely smooth and uniform. Begin adding the butter a little at a time and incorporating until smooth. Taste for seasoning and adjust the salt and pepper as needed. Transfer to a saucepan and keep warm until ready to serve. When ready, transfer to a serving dish and garnish with freshly chopped chives.