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Step 1
Prepare a charcoal grill or heat a gas grill. (Alternatively, use a cast-iron skillet or stovetop grill pan over medium-high heat.) Place swordfish steaks on a baking sheet and season on both sides with salt and pepper. Drizzle each with 1 teaspoon olive oil and rub with fingers to coat. Leave at room temperature.
Step 2
In a mixing bowl, put vinegar, smoked paprika, tomato paste and garlic. Stir to dissolve tomato paste. Add onion, sweet pepper, chiles and 4 chopped anchovy fillets, and stir everything together. Add pinch of salt and ½ to ¾ cup olive oil and stir again.
Step 3
Add cherry tomatoes, lightly season with salt and pepper, then gently fold them into the mixture. Leave to marinate about 10 minutes.
Step 4
Grill the swordfish steaks over medium-hot coals for about 4 minutes per side. Remove when you see juices begin to rise on second side.
Step 5
Transfer to plates or a large platter. Stir salsa and spoon generously over fish. Sprinkle with oregano. Garnish with whole anchovy fillets. Surround with a generous amount of arugula and serve.