Method

In 2 large skillets or shallow Dutch oven, heat oil over medium-high heat; cook mushrooms, thyme, salt and pepper, stirring often, for 10 to 15 minutes or until browned. Remove from heat.

Dressing:
Whisk together vinegar, oil, mustard, sugar and salt ; stir into mushroom mixture. Let cool slightly.

In salad bowl, toss together arugula, radicchio, mushroom mixture and Parmesan cheese.