Adjust oven rack to the lower-middle position. Preheat oven to 325°F. Season the beef cubes generously with salt and pepper and set aside at room temperature.
In a small food processor, combine the paprika, drained red peppers, tomato paste, and 2 teaspoons vinegar. Process until smooth. Set aside.
Pour the vegetable oil into a large Dutch oven set over medium heat on the stovetop. Add the mushrooms and cook, undisturbed, until browned on one side. Stir then add the onions and 1 teaspoon salt. Cover and cook, stirring occasionally until the onions are soft but not browned, about 8 to 10 minutes.
Remove the lid and add the garlic and thyme. Sauté until fragrant. Add the paprika mixture and cook for about 2 minutes, stirring constantly. Add the diced tomatoes with juice, the beef cubes, and 2 cups of the beef broth. Stir well to combine. Cover the pot and transfer to the oven. Cook until the meat is almost tender, about 2 hours, stirring half way through.
Add the potatoes and carrots if using. Add 1 cup (2 cups if needed to cover) of the remaining beef broth to the pot. Cover and return to the oven and cook for about 60 minutes, stirring halfway through until the beef and potatoes are tender. Remove from the oven.
Place the Dutch oven on the stovetop and heat on medium. Allow the stew to settle a minute then skim off and discard any fat that pools on top. Remove the thyme sprigs and discard. Mix the cornstarch with ¼ cup of the remaining beef broth. (SEE NOTES) Drizzle the slurry into the stew while stirring gently to combine. Heat for about 2 minutes or until slightly thickened. Off heat, stir in remaining 1 teaspoon vinegar. Check seasoning and add salt and pepper to taste.
Stir in the sour cream, if using, or serve each bowl garnished with a dollop of sour cream, parsley and fresh ground black pepper.