Heat half of the butter in a small saute pan, then add mushrooms, shallots and thyme. Season with salt and pepper, and cook down the mushrooms until they've lost most of their extra water. Remove from heat and set aside.
Coat a muffin tin with non-stick cooking spray. Cut tortillas into quarters. Press two tortilla quarters into each cup, with the points toward the center. The tortilla pieces should overlap to form cups.
Place a spoonful of the mushroom mixture into the bottom of each tortilla cups so there's an equal amount in each. Crack one egg in each cup, then sprinkle the tops with the grated cheese, parsley, salt and pepper.
Melt remaining butter. Brush all exposed edges of the tortillas with the melted butter.
Bake at 400 degrees for 12-15 minutes until the whites are cooked through and the yolks are as done as you like them to be. Serve either hot or at room temperature.