Pour oil into an 8-inch, straight-sided skillet. Heat over medium-low heat 8 minutes or until oil reaches 175° to 180°. Carefully add tomato halves and rosemary sprig. Cover and poach at a light simmer, adjusting heat as necessary, 10 minutes or until tomatoes are tender. (Keep heat on.) Remove tomatoes from skillet using a slotted spoon; place, cut-side down, in a shallow dish. Cool 10 minutes; set aside.
Sprinkle fish with kosher salt and 1/4 teaspoon pepper. Carefully place into hot oil. Cover and poach 6 to 10 minutes or until fish flakes with a fork. Transfer to a serving platter, and keep warm.
Remove skins from tomatoes; discard skins. Place tomatoes and any accumulated liquid in a food processor; pulse 3 times or until coarsely chopped. Transfer tomatoes to a medium bowl, and stir in olives, capers, chopped rosemary, vinegar, and remaining 1/4 teaspoon pepper. Serve over mahimahi. Garnish, if desired.
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