Pat the pork shoulder dry with paper towels and cut it into bite-sized cubes. Heat oil in a large pot and sear the pork until browned on all sides.
Add the onions and sauté until soft and lightly golden, about 5 minutes. Stir in the carrot and cook for another 8–10 minutes.
Season the vegetables with salt, black pepper, basil, oregano, thyme, and paprika. Stir to evenly coat.
Pour in the water or stock, stir well, cover, and let simmer for 10 minutes.
Add the garlic, bay leaves, and potatoes. Add more liquid if needed, cover, and simmer until the potatoes are tender, about 25 minutes.
Finally add tomato puree and cover the lid and cook for another 7 min. ( Optional )
Remove from heat, garnish with fresh parsley, and serve warm.