Warm the broth
In a medium pot, combine the chicken broth and clam juice. Heat gently and keep warm over low heat.
Prepare the seafood
Pat the fish and shrimp dry with paper towels. Season lightly with kosher salt and black pepper. Set aside separately.
Cook the aromatics
In a large heavy skillet, paella pan, or cast-iron pan, melt the butter over high heat. Add the onion and garlic and cook for 1 minute, stirring frequently.
Build the flavor base
Add cilantro, basil, and scallions and cook for another minute. Stir in smoked paprika, cayenne pepper if using, and chopped tomatoes. Cover and cook for 3–4 minutes until the tomatoes soften.
Add the broth
Pour the warm broth and clam juice mixture into the pan and bring to a boil. Season generously with salt and pepper.
Cook the rice
Sprinkle the Arborio rice evenly into the pan. Boil uncovered for 3 minutes, stirring occasionally, then smooth the rice into an even layer.
Add the fish
Arrange the fish pieces evenly over the rice, pressing them gently into the liquid. Do not stir after this point.
Simmer
Reduce heat to a gentle boil and cook uncovered for about 10 minutes until most of the liquid is absorbed. Add up to 1/4 cup extra broth if needed.
Add shellfish and shrimp
Arrange the mussels, clams, and shrimp evenly over the rice with shellfish facing upward. Continue cooking uncovered for 15 minutes until the shrimp are opaque, shellfish open, and rice is tender. Turn shrimp once halfway through cooking.
Rest and serve
Remove from heat, cover tightly with foil or a lid, and let rest for 10 minutes. Discard any unopened shellfish. Serve with lemon or lime wedges and extra cilantro if desired.