Cook the pasta according to the package directions. Reserve ½ cup of the cooking water, drain the pasta, and return it to the pot.
Meanwhile, heat the oil in a large skillet over medium-high heat.
Add the mushrooms and onion and cook, tossing occasionally, until the mushrooms begin to release their juices, 2 to 3 minutes.
Add the wine, ½ teaspoon salt, and ¼ teaspoon pepper and cook until the mushrooms begin to brown, 5 to 6 minutes.
Toss the pasta with the Brie and reserved cooking water until the pasta is coated. Stir in the mushroom mixture and arugula.