Heat the vegetable oil in a large pot over medium-high heat. Add the pork cubes and brown them on all sides for about 6 minutes. Remove the pork and set it aside.
Lower the heat to medium. Add the diced onion to the pot and cook until it softens, about 5 minutes. Stir in the minced garlic and cook for 1 minute more.
Stir the sweet Hungarian paprika and tomato paste into the onions until everything is evenly coated. Return the browned pork to the pot.
Pour in the beef broth, then add the bay leaf, salt, and black pepper. Bring the mixture to a simmer.
Add the potato cubes and carrot slices. Cover the pot and let it simmer gently for 45 minutes, stirring once or twice, until the pork is tender and the vegetables are cooked through.
Remove the bay leaf before serving. Ladle the stew into bowls and top each portion with a spoonful of sour cream and a sprinkle of chopped parsley.