Heat 2 tablespoons olive oil in a large, shallow skillet or paella pan over medium-high heat.
Add the chicken pieces and brown on all sides, about 5 to 7 minutes; transfer to a plate.
Add the chorizo and cook until crispy, about 3 to 5 minutes; transfer to the plate with the chicken.
Reduce heat to medium. Add the onion and red bell pepper and cook until softened, about 8 to 10 minutes.
Stir in the garlic and smoked paprika and cook until fragrant, about 1 minute.
Add the rice and stir to coat the grains, about 2 minutes.
Stir in the diced tomatoes, chicken broth, and saffron (if using); bring to a gentle simmer.
Arrange the chicken pieces evenly over the rice; do not stir. Simmer uncovered until most of the liquid is absorbed and a crust (socarrat) forms on the bottom, 15 to 20 minutes.
Scatter the chorizo and peas over the top. Cover the pan, remove from heat, and let rest for 5 to 10 minutes.
Fluff the rice with a fork. Season with salt and freshly ground black pepper. Garnish with chopped parsley and serve with lemon wedges.