Dumplings: Preheat oven to 350°F (180°C). Toss apple slices with brown sugar, butter, lemon juice and cinnamon. Unroll the crescent roll dough and separate each roll into four rectangles, sealing the perforations with your fingertips.
Divide the apples evenly, mounding in the center of each rectangle. Brush around the edges of the dough with some of the beaten egg. Bring the sides of the dough into the center and crimp edges to seal. Brush tops with remaining egg.
Line baking sheet with parchment paper. Transfer dumplings to prepared baking sheet. Bake for 20 minutes or until golden. Serve with brown sugar sauce.
Brown Sugar Sauce: Stir brown sugar with corn starch in a heavy saucepan. Stir in butter, lemon juice and boiling water. Cook on medium heat for 5 minutes, stirring often, or until bubbly and thickened. Set aside and keep warm.