Place the rack in center of the oven and preheat to 375°F Grease and flour a 9-inch springform pan. In a large bowl, with your fingertips, rub together the first measure of flour, the 1 1/2 cups sugar, salt, and butter until crumbly. Remove 1 cup of the crumbs and press them onto bottom of the springform pan and about 1/2-inch up the sides, making a crust about 1/8-inch thick.
Make a well in the remaining crumb mixture. Pour into it the milk, eggs, vanilla, lemon zest, the second measure of flour, and baking powder. With a whisk, blend this mixture thoroughly without incorporating the crumbs. Then with a wooden spoon stir in the crumbs until well blended but still a little lumpy. Fold in the apples. Scrape the batter into the pan.
Beat the egg white until foamy. Beat in the 2 tablespoons sugar until whites barely stand in peaks. Zigzag it over the top of the batter, leaving 2/3 of the batter uncovered.
Bake 65 to 75 minutes, or until a knife inserted in the center comes out clean.
Remove from oven and cool 30 minutes on a wire rack. Slip off sides of the pan and finish cooling cake. Serve at room temperature. Covered in plastic wrap, the cake holds well at cool room temperature for 2 days. It keeps a week in the refrigerator. Warming in the oven makes it even tastier.