With a rubber spatula, scoop the pate a choux into the pastry bag and pipe out approximately 16 (1 1/2-inch rounds) spaced 1 to 2 inches apart on the parchment paper-lined baking sheet. Brush lightly with the beaten egg and place in the oven. Cook until golden and puffed, about 25 minutes. Remove from the oven and cool on a baking rack.
Split the profiteroles nearly in half, leaving a little hinge at the back, and cradle a small scoop of vanilla ice cream inside each. Divide the profiteroles between bowls and pour over some chocolate sauce. Serve cold.