Heat a large skillet over medium-high heat and add olive oil.
Add the mushrooms to the hot skillet, cap side down. Allow them to cook until golden brown, about 5 minutes.
Flip them over and turn heat to medium. Add the salt, pepper, and crushed red pepper flakes if using.
Add the wine, garlic, shallots, and thyme. Allow the wine to come to a simmer. Let it cook until reduced by half and the mushrooms are tender, 6-8 minutes.
Stir in the lemon juice, making sure the mushrooms are fully coated in the sauce.
Remove the pan from the heat. Discard the thyme sprigs. Stir in the butter a tablespoon at a time until dissolved.
Sprinkle the parsley and parmesan over the top.
Notes
You can replace the white wine with dry Marsala or dry sherry.
This same recipe can be made without any wine. Use the same amount of chicken broth or vegetable broth.