Preheat oven to 400 degrees. Toss mushrooms in olive oil, 1/2 teaspoon salt and fresh thyme. Spread out onto a baking sheet in a single layer and roast for 15 minutes.
While mushrooms are roasting, bring a large pot of salted water to a boil. Once boiling, add the tortellini and cook according to package directions (should be about 15 minutes).
Whisk together all of the ingredients for the lemon vinaigrette.
Once mushrooms are done remove from oven and set aside in a separate bowl to cool.
Drain pasta and toss with a little oil and a few ice cubes to quickly cool (or you can place it in the fridge to cool).
Once pasta is cool, toss with roasted mushrooms, arugula, lemon vinaigrette and parmesan. Top with additional shredded parmesan and serve.