For crust and topping, in a medium bowl, beat egg yolk, brown sugar, butter, and salt with an electric mixer until well combined. Add 2 cups flour and beat on low until crumbly.
Press half of crumb mixture evenly into an ungreased 13x9x2-inch baking pan. Cover; reserve remaining mixture.
Bake in a 350 degree F oven for about 12 minutes or until lightly browned. Cool on a wire rack for 15 minutes.
For filling, in a small bowl, combine the 2 tablespoons flour, the granulated sugar, and cinnamon. Set aside.
In a microwave-safe bowl, combine caramels and water. Cover with vented plastic wrap and microcook on 100 percent power (high) for 1 to 1-1/2 minutes or until caramels melt, stirring once or twice. (Or heat caramels and water in top of a double boiler over gently boiling water 20 minutes; stir occasionally.)
In a large bowl, toss apple slices with the cinnamon mixture. Arrange the apple slices over the slightly cooled crust. Drizzle the melted caramel mixture evenly over apples. Crumble the reserved topping evenly over the caramel. Brush surface with egg white, if you like. Sprinkle with pecans.
Bake in a 350 degree F oven for 40 to 45 minutes or until the top is nicely browned, and apples are tender. Cool completely in pan on a wire rack. Cut into squares. Makes 24 servings.