Cook the tortellini in a large pot of salted boiling water according to package directions; drain, rinse with cold water to stop cooking, and set aside.
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 their liquid evaporates and they begin to brown.
Reduce heat to low, pour in the heavy cream, stir in the dried thyme and salt, and bring the mixture briefly to a simmer.
Add the cooked tortellini to the skillet and stir to combine evenly with the cream and mushrooms.
Sprinkle the shredded Mexican cheese blend evenly over the tortellini, cover with a tight lid, and cook on low for about 5 minutes until the cheese melts.
Uncover, garnish with chopped parsley, and serve immediately.
