Fill a large pot with water and 1 tablespoon olive oil; bring to a rolling boil. Stir in tortellini and cook until they float to the top and the filling is hot, approximately 7 minutes. Drain and transfer to a large bowl.

Melt 2 tablespoons butter in a large saucepan over medium-high heat. Saute mushrooms, onion, and garlic until the vegetables are soft, about 5 minutes. Remove the vegetable mixture with a slotted spoon and add it to the bowl with the tortellini.

Drain excess liquid from the saucepan. Reduce heat to medium and melt the remaining 6 tablespoons butter. Stir in half-and-half, salt, pepper, garlic powder, and cayenne. Cook, stirring occasionally, until thick and bubbly, approximately 10 minutes.

Gradually stir in Parmesan cheese until melted and the sauce is thickened.