- 1/2 cup mayonnaise
- 1 tablespoon fresh lemon juice
- 1 garlic clove, pressed
- 1 teaspoon (packed) minced fresh Italian parsley
- 1 teaspoon grated onion
- 1 teaspoon anchovy paste
- 2 hard-boiled large egg yolks
- 1/4 cup extra-virgin olive oil
- 2 tablespoons drained capers
- 1/4 cup olive oil
- 2 tablespoons tarragon vinegar
- 2 small bay leaves, broken
- 4 6-ounce ahi tuna steaks (each about 1 inch thick)
- Nonstick vegetable oil spray
- 4 4-inch square crusty artisanal rolls or squares of focaccia, split horizontally
- Whisk first 6 ingredients in bowl to blend. Using fine grater, grate in egg yolks. Whisk in oil, then capers. Season with salt and pepper.
- Do ahead: Can be made 1 day ahead. Cover and chill.
- Combine oil, vinegar, and bay leaves in large heavy-duty resealable plastic bag. Shake to blend. Add tuna. Seal bag; turn to coat. Chill at least 1 hour and up to 2 hours, turning bag occasionally.
- Spray grill rack with nonstick spray and prepare barbecue (medium-high heat). Brush cut sides of rolls with some of tuna marinade. Grill rolls, cut side down, until golden, about 2 minutes. Transfer rolls to work surface. Grill tuna, with some marinade still clinging, until slightly charred but still pink in center, about 2 1/2 minutes per side.
- Place tuna on roll bottoms. Top with dollop of sauce, then roll tops. Serve, passing remaining sauce separately.