In a straight sided stainless steel saucepan or a 28cm (11 inch) paella pan, heat oil over medium to high heat.
Season calamari and shrimp with salt and sear in the hot pan for 2 to 3 minutes. Remove from pan and set aside.
Add the sofrito, paprika, and saffron. Saute for 2 to 3 minutes until well mixed and sizzling.
Add the stock (or water) and bring the liquid to a rolling boil. Season with salt.
Sprinkle in the rice, and using your spatula gently swirl the liquid to distribute the rice evenly. Return the liquid to a boil and then reduce the heat to medium-low.
Cook, uncovered, for 8 minutes, without stirring.
Place shrimp, and calamari on the rice. Continue to cook the rice until the liquid has fully absorbed and the rice has softened, this may take about 10 to 15 more minutes. (See note 3).
Reduce heat to low, place the mussels on the rice and cover with a lid. Cook for a further 4 to 5 minutes or until the mussels are cooked. (see note 4).
Remove from heat and let it rest for 5 minutes before serving. Serve, garnished with chopped parsley and lime wedges, if desired.