Bring first 3 ingredients to boil in heavy medium saucepan over high heat, stirring to dissolve sugar. Reduce heat to medium-high and boil until reduced to 3/4 cup, about 14 minutes. DO AHEAD: Sauce can be made 5 days ahead. Cover and chill.
Pat filets mignons dry and season with salt and pepper. In a shallow roasting pan roast filets in middle of oven 12 minutes for rare or 20 minutes well done, and cool (filets will be baked again after being wrapped in pastry). Chill filets, covered, until cold, about 1 hour.
Thinly slice shallots in a heavy skillet cook in butter with garlic, and salt and pepper to taste over moderate heat, stirring, until cook through. Transfer shallot mixture to a bowl to cool completely.
In a small bowl lightly beat egg to make an egg wash. On a lightly floured surface roll out puff pastry sheet into a 14-inch square. Trim edges to form a 13-inch square and cut square into four 6 1/2-inch squares. Put 2 tablespoon Gorgonzola in center of 1 square and top with one fourth shallot mixture. Top mushroom mixture with a filet mignon, pressing it down gently, and wrap 2 opposite corners of puff pastry over filet, overlapping them. Seal seam with egg wash. Wrap remaining 2 corners of pastry over filet and seal in same manner. Seal any gaps with egg wash and press pastry around filet to enclose completely. Arrange beef Wellington, seam side down, in a non-stick baking pan. Make 3 more beef Wellingtons in same manner. Chill remaining egg wash for brushing on pastry just before baking. Chill beef Wellingtons, loosely covered, at least 1 hour and up to 1 day.
Preheat oven to 425°F. Brush top and sides of each beef Wellington with some remaining egg wash and bake 20 minutes, or until pastry is golden.