Fill a large pot with water and 1 tablespoon oil; bring to a rolling boil. Stir in tortellini and cook until they float to the top and the filling is hot, about 7 minutes. Drain and transfer to a large bowl.
Meanwhile, melt 2 tablespoons of butter in a large saucepan over medium-high heat. Saute mushrooms, onion, and garlic until the vegetables are soft, about 5 minutes. Use a slotted spoon to remove vegetable mixture from the pan and add it to the bowl with the tortellini.
Drain the excess liquid from the mushrooms from the saucepan. Reduce heat to medium and melt remaining 6 tablespoons butter. Stir in half-and-half, salt, pepper, garlic powder, and cayenne. Cook, stirring occasionally, until thick and bubbly, about 10 minutes. Gradually stir in Parmesan cheese until melted and sauce has thickened.
Pour the sauce over the tortellini and mushroom mixture, and toss to combine. Serve in bowls and garnish with fresh thyme.
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