Sprinkle lamb with salt and pepper. Pour 1 tbsp. olive oil into a large pot over medium-high heat. Working in batches, add lamb in a single layer; cook, turning as needed, until browned all over, 12 minutes per batch. Transfer to a bowl and add more oil between batches if necessary.
Reduce heat to medium; if pan is dry, add a little more oil. Add onion and cook, stirring occasionally, until soft, 5 minutes. Add garlic, paprika, and cumin and cook until fragrant, 2 minutes. Add wine, 1 1/2 cups broth, and the tomato paste; bring to a boil, stirring to scrape up browned bits. Add lamb and juices; cover and simmer, stirring occasionally, until lamb is very tender when pierced, 1 1/2 to 1 3/4 hours. Add more broth if mixture gets too dry.
Meanwhile, preheat broiler. Set pepper halves skin side up on a baking sheet. Broil 4 to 6 in. from heat until blackened all over, about 8 minutes. Remove from oven and let stand at least 10 minutes, then peel and thinly slice lengthwise. In a small bowl, mix parsley, olives, and capers.
Stir roasted peppers into lamb mixture. If stew is too thick, add a little more broth. Cook, uncovered, until heated through. Season to taste with more salt and pepper and top with parsley mixture.
Note: Nutritional analysis is per serving.