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Step 1
Line two large baking sheets with parchment paper; set aside. On a lightly floured work surface, roll out the dough to a 13-inch square, a little over a 1/4-inch thick. Using a ruler and a pizza wheel or pastry cutter, trim the edges of the dough to form a 12-inch square. Then cut the dough into nine 4-inch squares.
Step 2
Dollop about 1 tablespoon cheese filling into the center of each 4-inch square of pastry.
Step 3
To form each Danish, brush each corner with beaten egg, fold the upper right corner over the filling, about two-thirds of the way toward the opposite corner; press down firmly to seal. Bring the lower left corner up and over first fold, pressing down to adhere. (Be careful not to fold too tightly, or you may force out some of the filling.) Repeat with the remaining corners. Place the Danish on the prepared baking sheets. Cover with plastic wrap, and let rest in a warm place until dough is doubled in bulk, about 45 minutes.
Step 4
Preheat the oven to 375 degrees. Brush dough with the beaten egg; sprinkle with the granulated sugar, if desired. Bake, rotating halfway through, until evenly brown, 20 to 25 minutes. Transfer to a wire rack to cool. Serve warm or at room temperature. These are best eaten the same day they are made.