With a cleaver, heavy chef's knife, or kitchen shears, split the pheasant in half, then cut the thighs and legs from the breasts. Place the 4 pieces of pheasant in a 6 to 8-quart stockpot and cover with the water. Bring to a boil, skimming off the white foam as it rises to the surface. (Using a ladle and a circular motion, push the foam from the center to the side of the pot, where it is easy to remove). Lower the heat so the broth is at a slow simmer.
Meanwhile, remove the leaves from 3 springs of thyme, reserving the stems, chop, and reserve (you should have 1 teaspoon). Add the thyme stems and the remaining thyme sprig to the broth. Also add the coarsely chopped onion and carrot, the celery, garlic, bay leaves, peppercorns, and cloves, along with the reserved bacon rind, to the pot. Season lightly with salt, partially cover, and simmer slowly for 2 hours.
Remove the broth from the heat. With tongs, transfer the pheasant pieces to a plate. When they are cool enough to handle, pull the meat off the bones, discarding the bones, and tear the meat into bite-sized pieces. Or cut the meat with a knife into rectangular strips that are approximately 1/2 by 1-inch. (If you used whole pheasant, you will have about 1 pound of meat). Cover and refrigerate until needed. Strain the broth through a fine-mesh strainer; you should have about 8 cups. If you are not making the chowder right away, let the broth cool a bit, then refrigerate; cover the broth after it has chilled completely. (The broth and meat can be prepared a day in advance if you like)
Heat a 4 to 6-quart heavy pot over low heat and add the bacon. Once it has rendered a few tablespoons of fat, increase the heat to medium and cook until the bacon is crisp and golden brown. Pour off all but 1 tablespoon of the fat, leaving the bacon in the pot.
Add the butter, the diced onion, the sliced carrot, the reserved thyme leaves, and the caraway seeds and saute, stirring occasionally with a wooden spoon, until the onion is softened but not browned.
Add the potatoes and the reserved pheasant broth, bring to a simmer, and simmer over medium heat for about 8 minutes, until the potatoes are cooked through but still firm. Add the cabbage and simmer for 5 minutes more, until it just begins to soften (it will continue to cook after the chowder is removed from the stove).
Remove the chowder from the heat, stir in the pheasant meat, and season to taste with salt and black pepper. If you are not serving the chowder within the hour, let it cool a bit, then refrigerate; cover the chowder after it has chilled completely. Otherwise, let it sit at room temperature for up to 1 hour, allowing the flavors to meld.
When ready to serve, reheat the chowder over low heat; don't let it boil. Use a slotted spoon to mound the pheasant, cabbage, onions, and potatoes in the center of large soup plates or shallow bowls, and ladle the clear broth around. Sprinkle each serving with a generous spoonful of chopped parsley.