Pat chicken pieces thoroughly dry with paper towels. Season all sides lightly with salt and black pepper.
Heat 2 tablespoons avocado oil or olive oil in a large Dutch oven over medium-high heat until shimmering. Working in batches, sear chicken pieces without moving them, 3–4 minutes per side, until deeply golden brown on all sides. Transfer seared chicken to a plate and set aside.
Reduce heat to medium. Add 2 ounces finely chopped prosciutto to the pot and cook, stirring occasionally, until lightly crisp, about 2 minutes.
Add 1 medium yellow onion, diced, and 1 red bell pepper, diced. Cook, stirring occasionally, until softened, 4–5 minutes.
Stir in 4 cloves minced garlic and cook until fragrant, about 30 seconds.
Add 2 teaspoons adobo seasoning, ½ teaspoon smoked paprika, ½ teaspoon kosher salt, ¼ teaspoon black pepper, 2 bay leaves, ½ cup sliced green olives, 2 tablespoons drained capers, and ¼ cup chopped fresh cilantro. Stir to combine and cook 1 minute to bloom the spices.
Add 1½ cups rinsed long-grain white rice. Stir to coat rice in oil and spices, about 1 minute.
Pour in 3½ cups chicken stock. Add 1 pinch saffron or ¼ teaspoon turmeric, if using. Stir once to combine.
Nestle browned chicken pieces into the pot along with any accumulated juices. Bring to a gentle boil, then reduce heat to low. Cover tightly and simmer 20–25 minutes, or until rice is tender and most liquid is absorbed. Do not lift lid or stir during cooking.
If using frozen peas, scatter ½ cup over the top during the last 5 minutes of cooking. Cover and let warm through.
Check chicken for doneness — bone-in thighs and drumsticks should register 175°F on an instant-read thermometer. Remove bay leaves.
Remove pot from heat and let rest, covered, for 5–10 minutes. Fluff rice gently with a fork, taste and adjust seasoning, top with additional fresh cilantro, and serve.