Step 1In a small bowl, combine the shallots, lemon juice and vinegar. Set the bowl aside for 5 to 10 minutes to give the shallots time to quickly marinate. Add the salt and pepper, then the olive oil in a slow, steady stream, whisking constantly to combine. Stir in the mustard. Taste for seasoning and add more salt or pepper if desired. This makes about two-thirds cup vinagrette, which can be refrigerated in an airtight container up to 3 days. Bring the vinaigrette to room temperature and whisk to recombine the ingredients before using.
Step 1Remove the limp outer leaves from the radicchio and cut out the cores. Tear the radicchio leaves into roughly 11/2-inch pieces and place in a large bowl, discarding the white parts, which can be bitter. When you get closer to the core and the leaves are smaller, you won’t need to work around the white parts; you’ll use those, and the smallest leaves you won’t need to rip at all.
Step 2Sprinkle the radicchio with salt and give it a quick toss to distribute the salt. Drizzle with half of the mustard vinaigrette, massaging the vinaigrette onto the leaves to coat them thoroughly; add additional vinaigrette if desired, a tablespoon or two at a time. Taste and add more salt if desired.
Step 3Build the salad in 3 layers: Place one-third of the radicchio on a large platter or in a large wide-mouthed bowl. Scatter one-third of the cheese slices over the radicchio and repeat, building two more layers.