Cook the pasta according to package instructions, then drain and set aside.
While the pasta is cooking, cut the Brie into small pieces and thinly slice the shiitake mushrooms.
Heat a saucepan over medium-high heat and add the olive oil. Sauté the shiitake mushrooms for 3 minutes then add the minced garlic and cook for another minute.
Add the heavy cream to the saucepan and reduce the heat. Simmer the sauce for 5 minutes then add the Brie. Stir until the Brie has melted in the sauce.
Remove the saucepan from the heat, then add the pasta and the green peas. Season with a pinch of salt and pepper, to taste. Stir until the pasta is coated with the sauce.
Transfer the Brie pasta to plates and top with the grated Parmesan.