Whisk the miso, garlic, lemon zest and lemon juice with 2/3 cup of the oil in a bowl until smooth. Whisk in 1/4 cup water to thin out the dressing. Add 1 cup of the Parmesan and stir to combine. Season with salt and pepper.
Preheat a large grill pan or outdoor grill to medium-high heat. Cut the romaine and radicchio in quarters lengthwise, leaving some of the stem attached to each quarter. Brush the romaine and radicchio liberally with the miso Caesar dressing. Grill until the outer leaves are lightly charred, about 3 minutes total. Do not crowd the grill; grill in batches if needed.
Toss the shrimp with 1 tablespoon of the oil and sprinkle lightly with salt and pepper. Grill until slightly charred on both sides and just cooked through, 3 to 5 minutes total. Transfer to a mixing bowl and toss with 2 tablespoons of the miso Caesar dressing.
Brush the inside of the baguette with the remaining oil and sprinkle liberally with salt and pepper. Place cut-side down on the grill and cook until lightly charred and warmed through, about 3 minutes. Cut into 4 equal pieces.
To assemble, divide the grilled romaine and radicchio among 4 large plates. Scatter an equal amount of shrimp on each plate and sprinkle everything with the remaining Parmesan. Serve with the grilled bread and remaining miso Caesar dressing on the side.
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