To make the filling: Melt the 2 tablespoons unsalted butter over medium heat in a skillet large enough to accommodate the mushrooms. Add the minced shallot, and cook until it is translucent. Add the mushrooms, kosher salt and black pepper. Cook the mushrooms, stirring frequently, until they are tender, 5 to 8 minutes. Meanwhile, in a separate, heavy-bottomed saucepan, cook the wine over medium heat until it is reduced by half. Add the demi-glace and heavy cream. When the mushrooms are done cooking, strain any liquid that has accumulated in the pan into the pot with the wine, demi-glace and cream. Set the mushrooms aside.
Reduce the demi-glace mixture until a spatula will leave a trail when pulled across the bottom of the pot. Add this reduction and mushrooms to the cream cheese. Mix well. Refrigerate the filling for 2 hours or overnight before assembling the strudels.
To make the strudels: Lay the phyllo dough out flat on your table. Cover with a barely damp towel. Once you start working with the phyllo dough, you will want to work fairly quickly because it tends to dry out. Lay a sheet of phyllo dough on your work surface. Brush or dab it lightly all over with melted butter. Place another sheet of dough on top. Lightly dab it with butter as well. Repeat with a third phyllo sheet.
With a knife, cut the phyllo down the center, dividing it in half lengthwise. Place a heaping tablespoon of the filling on each half. Gently yet tightly roll the strudels up about 2/3 of the way. Fold the sides in to close the ends of the strudel, and continue rolling it up the rest of the way. You may need to add a little more butter to help seal the strudel. This should make 10 to 12 strudels. (It is OK if they look a little ragged; a homey, rumpled look is part of the phyllo mystique.)
You can make the strudels up to a day ahead to this point. If you do, wrap each strudel in wax paper, place in a single layer in a pan, cover tightly with foil or plastic wrap and refrigerate until you are ready to cook them.
To cook the strudels: Lightly spray a baking sheet with nonstick cooking spray. Arrange the strudels on the sheet so they are not touching one another. Lightly brush the tops of the strudels with a little melted butter or extra virgin olive oil.
Heat oven to 450 degrees, bake 4 to 6 minutes, turning pan once, back to front, to cook evenly. If not nicely browned at the end of baking, turn oven temperature down to 300 and bake 2 to 4 minutes more.