Set a large pot of salted water on the stovetop and bring to a boil. Cook the tortellini according to package directions, reserving 1/2 cup of the pasta water. Drain and set aside. Return the pot to the stove.
Set the heat to medium. Add the butter to the pot. Once melted, stir in the garlic, thyme, oregano, parsley, salt, and pepper. Cook for 30 seconds, just until fragrant.
Reduce the heat to low. Add the heavy cream and Parmesan. Cook for 5 minutes, stirring frequently, until the cheese is melted and the sauce is smooth.
Return the cooked tortellini to the pot. Stir gently to coat the pasta in the sauce. If the sauce feels too thick, add a splash of the reserved pasta water.
Adjust seasoning to taste. Sprinkle with additional parsley and serve hot.