Heat olive oil in a wide-bottomed pan. Sauté onions and garlic, browning slightly. Add the mushrooms and cook on medium heat until they become softened. Add thyme, salt, and pepper. Stir to combine.
In a small bowl, stir together half-and-half and cornstarch until smooth. Add mixture to the pan and bring to a simmer. Lower the heat and cook for an additional minute until slightly thickened.
Bring water to boil in a large stock pot. Salt and cook pasta according to package instructions before draining. Pour sauce over cooked pasta and serve.