Preheat oven to 375 degrees F. In a 10-inch oven-going skillet melt 1/2 cup butter over medium heat. Stir in apples and the 2/3 cup sugar. Cook over medium heat until bubbly, stirring occasionally. Reduce heat to medium-low. Cook, uncovered, about 20 minutes more or until apples are very tender, stirring occasionally. Remove from heat.
Meanwhile, in a medium bowl stir together flour and the 3 tablespoons sugar. Using a pastry blender, cut in 1/2 cup butter until pieces are pea-size. Using a fork, stir in egg and 1 to 2 tablespoons cold water until all of the flour mixture is moistened. Form into a ball.
On a lightly floured surface, use your hands to slightly flatten pastry. Roll pastry from center to edges into a 10-inch circle. Cut slits in the pastry. Roll pastry circle around the rolling pin. Unroll pastry over apple mixture in skillet, being careful not to stretch pastry. If necessary, carefully fold under edges of pastry.
Bake about 30 minutes or until the pastry is golden brown and filling is bubbly. Cool on a wire rack about 25 minutes before serving. If desired, serve warm tart with scoops of ice cream.