Step 1

Bring ½ inch water to boil in medium saucepan over medium-high heat. Using tongs, place eggs in boiling water (eggs will not be submerged). Cover and cook for 7 minutes. Transfer saucepan to sink and run cold water over eggs for 30 seconds to stop cooking.

Step 2

Peel and halve eggs. Transfer yolks to bowl (yolks will be jammy). Chop egg whites. To yolks, add 1 tablespoon extra-virgin olive oil, preserved lemon brine, mustard, and ½ teaspoon lemon juice and whisk until well combined. Stir in 1 tablespoon parsley, shallot, and egg whites. Season with salt and pepper to taste.

Step 3

In second bowl, combine preserved lemon, remaining 2 tablespoons extra-virgin olive oil, remaining 1 teaspoon lemon juice, and remaining 2 tablespoons parsley. Set aside.

Step 4

Slice tuna into 2-inch-wide strips. Rub ½ teaspoon vegetable oil into all sides of tuna strips and then sprinkle with salt. Sprinkle 1 side of each strip with pepper, pressing gently to adhere. Heat remaining ½ teaspoon vegetable oil in 12-inch carbon-steel or cast-iron skillet over high heat until just smoking. Sear tuna on 4 long sides, 30 seconds per side. Transfer to cutting board and immediately slice on bias ½ inch thick.

Step 5

Divide egg mixture evenly among bread slices and spread into even layer. Arrange tuna on top and garnish with parsley–preserved lemon mixture. Serve.