Heat the oven to 400 degrees. Toss butternut squash cubes with 2 TBS olive oil and bake in jelly roll pan until softened and starting to caramelize. Wipe out jelly roll pan and line with parchment paper.
While squash is roasting, heat remaining tablespoon of olive oil in large skillet over medium heat. Stir in garlic and shallot; cook 1 to 2 minutes. Add the mushrooms and remaining and increase heat slightly. Cook until mushrooms are soft and their juices evaporate, about 10 minutes. Stir in the wine and cook until the mixture is dry, about 5 minutes. Stir in the pepper and parsley. Season to taste with pepper and salt.
On a lightly floured surface, unwrap the defrosted puff pastry. Cut into 2 5-by-15-inch rectangles. Spread mushrooms on each pastry rectangle leaving 1/4-inch border. Spoon the cheese crumbles over the mushrooms. Then spoon the squash over the cheese, leaving a 1 1/2-inch border (it will look like a stripe of squash lying on a bed of cheese and mushrooms). Note - our frozen puff pastry was one large sheet, so we chose to make one pastry rather than two. Baking time remained the same as listed below.
Brush the exposed borders of dough on each rectangle with the egg wash. Fold the long sides up to meet in the middle and pinch together to seal; pinch the ends, too. Transfer the pastries to the baking sheet and turn them over so that the seam is face down. Brush the tops with more egg wash. Bake until they are puffed golden, and firm to the touch, about 30 minutes. Let cool for 10 minutes, slice and serve. 6 to 8 servings.