Slice the radicchio into wedges and drizzle with olive oil, balsamic vinegar, and pinches of salt and pepper. Grill each side for about 3 minutes, or until char marks form and the radicchio softens.
Remove from the grill and assemble the radicchio wedges on plates with a small handful of salad greens. Drizzle with olive oil and a little bit of balsamic vinegar. Top with the toasted hazelnuts and shavings of Parmesan cheese. Serve with freshly ground black pepper.
If desired, make toasted bread crumbs: Toast 2 slices of grainy bread until crispy. Rub with the cut side of a half clove of garlic, place in a food processor, and pulse into coarse crumbs. Sprinkle onto the salads.
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