Cook pasta according to package directions. Meanwhile, in a large skillet, saute the sausage, mushrooms, and garlic in butter.
Combine cornstarch and milk until smooth. Gradually add to the skillet. Bring to a boil, cook and stir 2 minutes or until thickened. Drain pasta, add to the sausage mixture. Stir in the peas and the cheese, cook until the cheese is melted.