Cook pasta according to package directions. Drain in a colander then drizzle with 1 teaspoon olive oil and toss to coat. Set aside.
Into the now-empty pot used for cooking the pasta, set the heat to medium-high, and add the remaining 2 tablespoons of olive oil. When the oil is hot, add the onions and cook for 1 minute. Stir in the mushrooms, salt, and pepper, and cook for 2 minutes, until lightly browned. Add the peas and sun-dried tomatoes, stirring frequently for 1 minute then add the garlic, cooking for an additional 30 seconds.
Stir in heavy cream, mushroom broth, Parmesan cheese, and Italian seasoning. Continue cooking, stirring frequently, until the sauce has thickened slightly.
Add the cooked pasta and toss to coat. Adjust seasoning to taste, sprinkle with parsley and additional Parmesan cheese, and serve hot.