Step 1

Stir tomatoes, olives, parsley, capers and brine, 1 tablespoon oil, and ¼ teaspoon each salt and pepper in a bowl until well combined. Let stand at room temperature until tomatoes start to release their juices, about 10 minutes.

Step 2

Meanwhile, heat 1 tablespoon oil in a large cast-iron or nonstick skillet over medium-high until shimmering. Season tuna steaks with remaining 1 teaspoon salt and ½ teaspoon pepper. Add tuna to skillet and cook, flipping once, until desired degree of doneness, 1 to 1½ minutes per side for rare. Transfer to a plate.

Step 3

Reduce heat to medium and add shallot to skillet; cook, stirring constantly, until softened, about 30 seconds. Remove skillet from heat and stir in vinegar, mustard, and remaining 3 tablespoons oil.

Step 4

Cut tuna across the grain into ½-inch-thick slices. Serve tuna with tomato-olive relish. Drizzle with warm shallot vinaigrette.