Prepare an ice-water bath. Bring a medium pot of salted water to a boil. Working in batches, add cauliflower, and cook for 1 minute. Using a slotted spoon, transfer to ice-water bath. Let cool. Transfer to a large bowl.
Return water to a boil. Working in batches, add beans, and cook until they start to turn bright green, about 30 seconds. Using a slotted spoon, transfer to ice-water bath. Let cool. Thinly slice beans on the bias. Transfer to large bowl, and add radicchio.
In a blender, process anchovies, lemon zest and juice, mustard, and garlic until smooth. With machine running, pour in oil in a slow, steady stream, blending until emulsified. Season with salt and pepper.
Pour dressing over vegetables. Stir in grated Parmesan. Season with salt and pepper. Let stand for at least 10 minutes. Garnish with shaved Parmesan.