Puree cherry tomatoes and clam juice in a blender until smooth. Press mixture through a fine-mesh strainer into a bowl.
Combine 3 tablespoons olive oil, green onions, garlic, anchovy, and 1 pinch red pepper flakes in a cold plan. Place over medium heat. Cook and stir until garlic and onions just start to soften, about 3 minutes. Stir in the tomato mixture. Bring to a simmer over medium-high heat. Reduce heat to medium and simmer stew until color deepens, about 10 minutes.
Add halibut and shrimp to the stew. Season with salt. Increase heat to high. Cover pan and cook until fish flakes easily with a fork, about 5 minutes. Stir in parsley, basil, oregano, and rosemary. Pour stew into a warm bowl. Drizzle in remaining olive oil and sprinkle 1 pinch red pepper flakes on top. Serve with crusty bread.
Any tomato product will work in this, but I really like cherry tomatoes here, since they provide a fragrant freshness you just won’t get with a can or jar. You do need to strain them after blending, but the few extra minutes of work will be well worth the effort.
Fish stock or chicken broth can be substituted for the clam juice.
Use any mix of white fish and shellfish that works best for you. If your shrimp is small, add it after larger chunks of seafood have already started cooking.
You can use 2 tablespoons of any combination of the Italian herbs mentioned.
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