PreparationFor sauce: 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. 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.
PreparationFor sauce: 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. 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.