Heat olive oil in a large deep skillet over medium heat. Add the chicken and season with salt and pepper. Cook until browned on all sides, about 5–6 minutes. Add the sliced chorizo and cook for 2–3 more minutes, until it starts to crisp. Remove both from the skillet and set aside.
In the same skillet, add the chopped onion and bell pepper. Sauté for 4–5 minutes until softened. Stir in the garlic and cook for another minute.
Add the rice to the skillet and stir for 1–2 minutes to lightly toast it. Sprinkle in the smoked paprika, turmeric (or saffron), and a pinch more salt and pepper. Stir to coat the rice evenly in the spices.
Pour in the warm chicken broth and stir to combine. Return the chicken and chorizo to the skillet, nestling them into the rice. Reduce heat to low, cover, and simmer for about 20 minutes, or until the rice is tender and most of the liquid has been absorbed.
Stir in the frozen peas during the last 5 minutes of cooking. Once everything is cooked, squeeze fresh lemon juice over the top and sprinkle with parsley.
Serve warm with extra lemon wedges on the side. Let the paella rest for 5 minutes before digging in to allow the flavors to fully meld.