Prepare the pork. Cut the pork shoulder into 1½-inch pieces and pat dry with paper towels. Season with 1 teaspoon of salt and the black pepper, tossing to coat evenly.
Brown the pork. Heat the olive oil in a large, deep skillet or Dutch oven over medium-high heat. Sear the pork in batches for about 6–8 minutes per batch, turning until browned on several sides. Transfer to a plate and set aside.
Cook the vegetables. Reduce the heat to medium. Add the butter and onions to the same skillet. Cook for 7–8 minutes, stirring occasionally, until softened and lightly golden. Add the red bell pepper and cook for another 4–5 minutes. Stir in the chopped tomato and garlic and cook for about 2 minutes more.
Build the paprika sauce. Remove the skillet from the heat and stir in the sweet Hungarian paprika for about 15–20 seconds. Pour in the chicken stock, scraping up any browned bits from the bottom of the skillet.
Simmer the pork. Return the pork and any accumulated juices to the skillet. Bring to a gentle simmer, cover, and cook over low heat for about 60 minutes, or until the pork is fork-tender. Stir occasionally, adding a little extra stock if the sauce reduces too much.
Prepare the sour cream mixture. In a small bowl, whisk together the sour cream and flour until smooth. Gradually stir in 3–4 tablespoons of the hot paprika sauce, mixing well to temper the sour cream.
Finish the paprikash. Reduce the heat to very low and gently stir the sour cream mixture into the skillet. Cook for another 10 minutes at a very gentle simmer, stirring occasionally, until the sauce is smooth and slightly thickened. Avoid vigorous boiling. Taste and add up to ¼ teaspoon of salt if needed, depending on the saltiness of your chicken stock. Garnish with fresh parsley and serve warm.