Cut the pork shoulder into bite-sized pieces and pat it dry with paper towels.
Heat 2–3 tablespoons of oil in a large deep skillet over medium-high heat. Add the pork in batches and sear until nicely browned on all sides, about 3–5 minutes per side. Transfer the pork to a plate.
In the same pan, add a bit more oil if needed. Cook the onion until soft and lightly golden, then add the carrots and cook until they begin to soften. Stir in the bell peppers and cook for another minute or two.
Return the pork (along with any juices) to the pan. Season with salt, black pepper, paprika, garlic powder, basil, and bay leaves. Stir everything together so the pork and vegetables are evenly coated.
Add the potatoes and pour in enough water or broth to mostly cover them. Bring to a gentle simmer, cover, and cook on low for about 30 minutes, until the potatoes are tender and the sauce has thickened slightly.
Turn off the heat and stir in the chopped dill and parsley. Cover and let the stew rest for 10–15 minutes before serving so the flavors can fully come together.