Spring Veggie Pasta

Name: Spring Veggie Pasta
Ingredients: 1/2 pound brussels sprouts; cleaned and cut in half; olive oil; salt and pepper; 1/2 pound pasta shells; 1 cup fresh shelled peas; frozen is fine too if that's what you have; 1-2 cups mushrooms; sliced and sauteed I recommend cremini; 1/2 cup heavy cream; 2 tablespoons unsalted butter; freshly ground black pepper; kosher salt; 1-2 teaspoons finely grated fresh lemon zest; 1 cup finely grated Parmesan cheese + more if needed for garnish; 2 tablespoons chopped fresh flat-leaf parsley or fresh chives