Ingredients

• 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

Instructions

1. 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.
2. Do ahead: Can be made 1 day ahead. Cover and chill.
3. For burgers: 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.
4. 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.
5. 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.
6. Place tuna on roll bottoms. Top with dollop of sauce, then roll tops. Serve, passing remaining sauce separately.