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Preheat the oven to 300°. Spread the bread on a large rimmed baking sheet and bake for 10 minutes, or until slightly crisp. Let cool; transfer to a large bowl.
In a large saucepan, combine the ham hock, thyme sprigs, garlic, bay leaf and water and bring to a boil. Cover and simmer over moderately low heat until the hock meat is very tender, about 1 1/4 hours. Remove the hock from the saucepan; pull off and coarsely shred the meat and discard the fat. Strain the broth and skim off the fat. You should have about 2 cups of the ham broth.
Meanwhile, in a large, deep skillet, cook the bacon and andouille over moderately high heat, stirring occasionally, until browned, about 10 minutes. Using a slotted spoon, transfer the meats to a plate. Pour off all but 2 tablespoons of the fat in the skillet. Add the onion and chopped thyme to the skillet and cook over moderate heat, stirring occasionally, until the onion is softened, about 10 minutes. Add the wine and cook until almost evaporated, about 10 minutes.
Preheat the oven to 350°. Return the bacon and sausage to the skillet. Add the shredded hock meat, sauerkraut and caraway seeds and cook over moderate heat for 5 minutes, stirring frequently. Add 1 cup of the ham broth and simmer for 5 minutes. Stir in the butter until melted. Add the mixture in the skillet to the bread cubes and toss to combine. Add the remaining 1 cup of ham broth and the Rich Turkey Stock and toss. Season with salt and pepper and let cool, then stir in the eggs. Generously butter a shallow 3-quart baking dish. Spread the stuffing in the dish in an even layer. Cover with buttered foil.
Bake the bread pudding for 30 minutes. Remove the foil and bake for 30 minutes, or until the center is cooked through and the top is crisp.
The baked bread pudding can be refrigerated for up 2 days. Bring the bread pudding to room temperature and reheat before serving.