In a pot, bring the chicken broth and EVOO, 1 turn of the pan, to a boil. Add the rice, cover, lower the heat and simmer for 15 minutes.
Using a food processor, puree the piquillo peppers. Stir the puree into the rice along with the parsley and paprika. Cover, turn off the heat and let stand for 5 minutes.
Meanwhile, in a large skillet, heat a drizzle of EVOO over medium-high heat. Add the chorizo and cook until crisp, turning, about 2 minutes on each side. Transfer to paper towels to drain. Add the chiles, onion and garlic to the skillet and cook until tender, about 5 minutes. Stir in the tomatoes and beans; season with salt and pepper.
Serve the rice in shallow bowls topped with the beans and chorizo.