Season the lamb neck pieces with salt and black pepper on all sides.
Heat the olive oil in a large Dutch oven over medium heat. Brown the lamb in batches until it develops color on all sides, then remove it to a plate.
Add the onion and garlic to the pot. Cook until the onion softens and turns translucent.
Stir in the chorizo slices and red bell peppers. Cook for a few minutes until the chorizo releases some of its fat.
Sprinkle in the smoked paprika and saffron threads. Add the bay leaf and stir everything for one minute to toast the spices.
Return the lamb to the pot. Pour in the broth and diced tomatoes. Bring the mixture to a gentle simmer.
Cover the pot and cook on low heat for about two hours, or until the lamb neck is very tender and pulls easily from the bone.
Taste the broth and adjust salt and pepper if needed. Remove the bay leaf before serving. Sprinkle with chopped parsley.