Cut away outside tough membrane from gizzard. Trim off end of heart, then chop finely with heavy knife. Chop liver separately.
Heat butter in pan, add onion and garlic. Cook until wilted, add gizzard, heart, thyme, cook stirring often, about 5 minutes.
Sprinkle with flour and stir. Add broth, water, bay leaf, salt, pepper and tomato paste; stir to blend. Let simmer over very low heat, stirring often and skimming surface of fat and scum, about 1 1/2 hours or until reduced to about 3 1/2 cups.
Combine gravy with turkey basting juices in roasting pan as directed in recipe for roast stuff turkey.