1. Bring a large pot of water to a boil. Hold a bunch of parsley by the stems, and starting at the top of the bunch, coarsely cut the parsley crosswise until you reach the thicker part of the stems; discard the stems. Repeat with the remaining bunches. Wash the chopped parsley in a large bowl of water, then drain. Add salt to the boiling water, then add the parsley and cook until tender, about 4 minutes. Drain well.
2. Preheat the oven to 350°. In a large saucepan, melt 1 tablespoon of the butter. Add the onion, cover and cook over low heat until softened, about 8 minutes. Add the garlic, increase the heat to moderate and cook until fragrant, about 3 minutes. Add the stock and simmer until reduced by half, about 8 minutes. Add the cream and country ham and simmer for 5 minutes. Stir in the cooked parsley and hominy, cover and simmer over low heat, stirring occasionally, until warmed through, about 8 minutes. Season with salt and pepper and transfer to a 9-by-13-inch glass baking dish. Cover with foil.
3. Bake the hominy for about 20 minutes, or until bubbling. In a small bowl, toss the bread crumbs with the melted butter. Turn the broiler on. Sprinkle the bread crumbs over the hominy and broil for about 1 minute, or until the crumbs are golden brown. Serve piping hot.
Make Ahead: The recipe can be prepared through Step 2 a day ahead.