Combine a large pinch of saffron threads with 1 tablespoon of chicken broth to let it infuse. Set aside.
Season the chicken with salt and pepper on both sides. Heat about 2 tablespoons of olive oil in a large 12-inch skillet (one with a lid) over medium heat. Cook the chicken about 6 to 8 minutes per side, until browned. Remove from the skillet and transfer to a plate. It doesn't need to be completely cooked through at this point.
To the same pan (do not wipe), add a few more drizzles of oil. Then add the onions, bell peppers, garlic, and smoked paprika. Sauté until fragrant and soft, about 5 to 6 minutes. Add sliced Spanish chorizo and cook for about 3 more minutes, stirring occasionally, until fragrant and slightly browned.
Add the rice and canned diced tomatoes. Stir to combine for about 2 minutes.
Stir in the 3 cups of chicken broth and saffron threads along with the broth it was infused in. Add salt and pepper to taste, and stir to combine. Bring to a light boil and then reduce to a simmer.
Return the chicken to the pan, nesting it under the broth. Add the frozen peas on top. Cook, covered, for about 25 minutes on low heat, until the rice is tender and the chicken is fully cooked through. Tip: Once it comes to a simmer, let the rice cook undisturbed, do not stir constantly. Stirring will cause it to have the consistency of risotto.
Remove from heat and let it sit for 5 to 10 minutes before serving, with the lid covered. During this time, the rice will absorb the remaining liquid and flavors. Serve with parsley and lemon wedges. I'd highly recommend a squeeze of lemon juice to amplify flavors. Enjoy!