1. In a 4-quart casserole, heat the lard until a light haze forms over it. Add the pork and, over high heat, turning it with a fork, brown it on all sides about 10 or 15 minutes altogether-then remove it and set it aside. Preheat the oven to 350°.
2. Pour off all but a thin film of the fat and add the onions. Cook them about 8 minutes over medium heat, or until they are lightly colored. Add the carrots and cook 2 or 3 minutes longer.
3. Off the heat, stir in the paprika. Continue to stir until the vegetables are coated. Pour in the stock and bring it to a boil, stirring in any brown bits that cling to the bottom and sides of the pan.
4. Return the pork to the pan, fat side up, salt and pepper it, and bring the liquid to a boil again. Cover tightly and braise the pork in the middle of the oven for 1½ hours, or .until thoroughly cooked and tender. Baste it occasionally with the pan juices.
5. Transfer the pork to a heated platter. Pour the contents of the pan into a sieve set over a saucepan, pressing down hard on the vegetables before discarding them. Skim off as much of the surface fat from the pan liquid as possible and bring the sauce to a simmer on top of the stove.
6. With a wire whisk, beat the flour and sour cream together in a bowl, then beat the mixture into the pan. Bring the sauce to a simmer once more and add the parsley, capers and caraway seeds. Taste for seasoning.
7. Carve the pork into ¼-to ½-inch slices and serve with some of the sauce poured over them and the rest passed separately in a sauceboat.
