Coarsely grate tomatoes into a bowl and discard skins. Put onion and bell peppers in another bowl. Measure garlic, paprika, and salt into a small bowl. Put rice in a bowl, seafood in another, and chorizo in a third.
Heat a grill to medium (350° to 450°). Meanwhile, toast saffron in a large saucepan over medium heat on a stove, stirring, until fragrant, about 2 minutes. Add 6 cups broth and the wine, cover, and bring to a boil over high heat. In a small covered saucepan, bring remaining 3 cups broth to a boil. Carry all ingredients, a 17- to 18-in. paella pan, a long-handled wooden spoon, a slotted spoon, and oven mitts to the grill.
For charcoal, add 15 briquets to fire just before cooking and cook with lid off until step For gas, keep lid closed as you cook. Heat paella pan on grill. Add 3 tbsp. oil, then chorizo, and brown the sausage, stirring, about 5 minutes. Using slotted spoon, transfer chorizo back to bowl.
Sauté onion and peppers in pan until onion is softened, about 5 minutes. Stir in tomatoes and cook, stirring often, until liquid evaporates and paste turns a shade darker, 10 to 12 minutes. Stir in remaining 1/4 cup oil and the garlic mixture; cook, stirring, 30 seconds. Stir in rice until evenly coated, then pat out level.
Carefully pour hot saffron liquid over rice and scatter chorizo on top. Check to be sure grill and liquid in pan are level. If needed, reduce gas or airflow in vents on lid and at base of grill (for charcoal grill) to maintain a steady simmer. Cook 12 minutes.
Pour enough hot plain broth over paella so rice is just covered in liquid (you may not use it all). Arrange mussels around rim of pan, almost touching, pushing them into liquid. Arrange any remaining mussels, the clams, and then the shrimp over paella in liquid.
Cover grill and cook paella until clams and mussels open (discard any that are unopened) and rice is al punto (al dente), another 6 to 10 minutes. Carefully remove paella from grill and set on a heatproof spot. Drape with paper towels and let stand about 5 minutes. Sprinkle with parsley and serve with Allioli.
*Find paella pans at kitchenware stores or online. Look for Spanish paprika, rice, and chorizo (not soft Mexican-style chorizo) in well-stocked grocery stores or online.
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