Add the olive oil to a frying pan and sauté the peppers over high heat, stirring for 1 minute. Set aside.
Heat a sauté pan and cook the chorizo over medium heat for a few minutes on both sides. Remove the chorizo from the pan and set aside.
Pour out the excess fat from the pan, but do not clean it. Add the onion to the pan and cook for a few minutes until soft.
Add the tomato paste and cook for 1 minute. Then, add the rice and cook for another minute, stirring occasionally. Deglaze with the white wine.
Add the garlic, peppers, and tomatoes. Pour in enough broth to just cover the rice. Cook the rice over low heat until tender, adding more broth as needed to keep it moist—this process takes about 18 minutes in total.
When the rice is nearly cooked, add the chorizo, heat it through, and stir a few times to combine.
Just before serving, add the mussels and season with freshly ground black pepper and a splash of lemon juice to taste. Divide the rice among four deep plates and garnish with cilantro.