Preheat your oven to 400 degrees. Wash and cut the brussels sprouts in half. Mix the brussels sprouts in olive oil and season with salt and pepper. Bake - cut side down- for about 15 minutes or until lightly browned and crispy.
While the oven is pre-heating, heat a pan with a little olive oil and sauté your sliced mushrooms. Season with a little salt and pepper.
Bring a large pot of salted water to boil. Add the pasta, and cook according to package directions. Add the peas to cook during the last 30 seconds of the pasta cooking time. Reserve about 1/2 cup of the cooking water. Set aside. Drain the pasta and the peas together.
In the same pot, bring the heavy cream to a simmer and heat for just a couple minutes, stirring frequently. Add the butter, and stir it until it has melted. Season the sauce with freshly ground black pepper, add a pinch of salt and the lemon zest. Add about 3/4 cup of the Parmesan, and stir it until the sauce is smooth. Add the drained pasta, peas and cooked mushrooms. Mix well until the sauce has coated everything evenly. Add the reserved pasta water by the spoonful only if needed to loosen up the sauce. Lastly, add the roasted brussels sprouts and toss/mix lightly.
Divide the pasta among bowls. Garnish with remaining Parmesan and chopped parsley or chives.