In a kettle of boiling salted water cook pasta until al dente. While pasta is cooking, in a large non-stick skillet heat 3 tablespoons oil over moderately high heat until hot but not smoking and saute all mushrooms with salt and pepper to taste, stirring occasionally, until golden brown. Add garlic and 3 tablespoons vinegar and cook, stirring, 1 minute. Add broth and simmer 3 minutes.
Drain pasta in a colander and stir into mushroom mixture. Toss mixture and remove skillet from heat. In a large bowl whisk together mustard, remaining tablespoon oil, and remaining 6 tablespoons vinegar until blended. Add radicchio and toss to coat with dressing. Add pasta mixture and Parmesan and toss well.
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