In a pot, melt butter and add the giblets to it. Cook them until they are brown.
Then, add the onions, celery, and carrots to it. Saute them for about 3-4 minutes until the onions become translucent. After that, add the garlic and saute for another minute.
Add bay leaf, thyme and water to the pot. Bring it to a boil and then, lower the heat. Cover the pot with a lid and cook on low heat for about 2 hours.
Then, drain the giblets through a sieve and save half a cup of the stock. Mince the giblets.
When your chicken or turkey is roasted, transfer its drippings to a pan.
Add flour to it and cook until it becomes thick. Then, add the stock and the inced giblets to it. Stir it until it becomes thick.
Season it with salt and pepper. If you want a smoother gravy, you can blend it. Otherwise, if you like chunky gravy, then your gravy is ready!