1.Mix the flour and 1/4 teaspoon salt together in a food processor. Add 1/2 cup butter and pulse a few times until the butter is in small pieces. Add 1 egg and then add the milk gradually and continue pulsing until a lumpy dough forms.
2.Form the dough into a large ball, flatten slightly into the shape of a disk, cover with plastic wrap, and refrigerate for at least 1 hour or until ready to use.
3.Heat a large skillet over medium heat, add 1 tablespoon butter, and saute the shallot for about 6 minutes. Then add the mushroom, thyme, and garlic to the shallot and saute for another 7 minutes.
4.Increase heat to medium high and add the white wine, 1/2 teaspoon salt, pepper, and heavy cream and heat for about 3 minutes. Transfer to a bowl and mix in parsley and truffle oil, then set aside to cool completely.
5.Take the dough out of the refrigerator and roll into a log. Cut into 12 equal pieces. Preheat the oven to 400 degrees and place parchment paper on top of a sheet pan. In a small bowl beat 1 egg and set aside.
6.Take one dough ball and roll it out into a thin round. Place about a tablespoon of mushroom mixture inside, top with some cheese, and fold the circle over. Pinch the edges together with a fork, then repeat with the rest of the dough.
7.Place on baking sheet and lightly brush the tops with the egg wash. Bake for 15-20 minutes or until golden brown. Serve immediately.