Bring a large pot of salted water to a boil and cook the tortellini according to package directions; drain, rinse under cold water, and set aside.
While the tortellini cooks, heat a large skillet over high heat and add the butter.
Add the sliced mushrooms and sauté on high for about 10 minutes, stirring occasionally, until the liquid evaporates and the mushrooms begin to brown.
Reduce heat to low, pour in the heavy cream, stir in the dried thyme and salt, and bring the mixture to a gentle boil.
Add the drained tortellini to the skillet and toss to coat evenly with the cream and mushrooms.
Sprinkle the shredded Mexican cheese blend evenly over the tortellini, cover with a tight-fitting lid, and cook for about 5 minutes until the cheese melts.
Garnish with chopped parsley and serve immediately.