Season the pork with black pepper. Heat 2 tablespoons of oil in a large deep skillet over medium-high heat.
Add the pork in a single layer and let it brown before turning. Cook it in batches if needed so the pieces sear instead of steaming. Transfer the browned pork to a plate.
Add the diced onion to the same skillet and cook for 4 to 5 minutes, until softened and lightly golden.
Stir in the garlic and tomato paste. Cook for about 1 minute, stirring often, until the tomato paste darkens slightly and smells rich and savory.
Pour in the water or broth and scrape up the browned bits from the bottom of the skillet. Add the diced pickles, bay leaf, and dried thyme.
Return the pork to the skillet and bring the sauce to a gentle simmer. Cover and cook over low heat for 35 to 45 minutes, until the pork is tender.
While the pork simmers, heat 3 tablespoons of oil in a separate skillet over high heat. Add the potato wedges and fry for about 8 minutes, turning them occasionally, until lightly golden around the edges. The potatoes do not need to be fully cooked yet.
Add the fried potatoes to the pork and tomato sauce. Sprinkle in the paprika and 1/2 teaspoon salt, then gently stir everything together.
Cover and continue cooking for 15 to 20 minutes, until the potatoes are tender and have absorbed some of the tomato and pickle sauce. Add a small splash of water if the sauce becomes too thick before the potatoes are ready.
Remove the bay leaf, taste, and add more salt only if needed. Finish with fresh parsley and let the stew rest for 5 minutes before serving.