Special equipment: Eight 10-inch wooden or metal skewers
Whisk the mayonnaise, 1/4 cup of the oil, the anchovies, garlic, lemon zest and juice and 1/2 teaspoon freshly ground black pepper together in a mixing bowl. Add 1 cup of the Parmesan and stir to combine. Season with some salt and pepper.
Preheat a large grill pan or outdoor grill over high heat. Slice the baguette in half length-wise, like you would to make a sandwich. Then slice each half into 8 equal pieces, about 3/4-inch-thick. Place the pieces on a baking sheet or large plate and reserve.
Quarter the romaine hearts lengthwise and cut each quarter into 1-inch pieces, making sure to keep each piece stacked and together. You will need 24 pieces total.
To assemble the skewers, carefully thread 1 stack of the romaine on a skewer, making sure that the thickest part of the romaine is in the center of the skewer. Follow the romaine with 1 piece of baguette and repeat until you have 3 stacks of romaine and 2 pieces of baguette on the skewer. Thread 2 shrimp onto the end of the skewer, making sure that both the top and bottom of each shrimp is taut on the skewer. Leave no more than 1/2-inch of exposed skewer at each end once all of the ingredients are on. This will prevent you from having to soak the skewers if you are using wooden skewers. Place the assembled skewer on a sheet tray. Repeat with the remaining 7 skewers and ingredients.
Place 1/2 cup of the dressing in a small bowl and whisk in the remaining oil. Brush the skewers liberally with the dressing. Place the skewers on the grill and cook until the bread and romaine are lightly charred and the shrimp is just cooked through, about 3 minutes, rotating the skewers as needed for even charring. If the shrimp is not cooked by the time the bread toasts, use tongs to touch the shrimp ends to the hot grill grate.
Transfer the grilled skewers on to a large platter and sprinkle with the remaining Parmesan. Serve immediately with the remaining dressing on the side.
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