Bow-Tie Pasta with Sausage, Peas, and Mushrooms

Heat 2 tablespoons olive oil in a large skillet over high heat; cook and stir sausage in the hot oil, breaking up any large chunks, until browned and crumbly, about 5 minutes. Transfer cooked sausage to a plate. Heat 2 more tablespoons olive oil in the same large skillet over medium heat; cook and stir mushrooms, 1/2 teaspoon salt, and 1/2 teaspoon pepper in the hot oil until mushrooms are tender and all the liquid has evaporated, about 8 minutes. Stir peas into mushroom mixture and cook until peas are warmed, about 2 minutes. Return sausage to mushroom mixture; cook and stir until flavors have blended and sausage is heated, about 3 minutes. Bring a large pot of lightly salted water to a boil. Cook bow-tie pasta at a boil, stirring occasionally, until cooked through yet firm to the bite, about 12 minutes; drain pasta, reserving 1/2 cup pasta water. Return pasta to pot and stir in sausage-mushroom mixture; cook and stir, adding reserved pasta water as needed, until mixture is evenly mixed, about 5 minutes. Drizzle remaining 1/4 cup olive oil over pasta mixture and season with remaining 1/4 teaspoon salt and 1/4 teaspoon pepper; toss to coat. Add Parmesan cheese; toss to combine.