1 Heat oven to 350º F / 175º C. Grease a 9 inch square pan.
2 Melt 1 tablespoon butter in a skillet. Add the apple slices and saute over medium high heat for 2-3 minutes; stirring often. Set apples aside to cool.
3 Sift 1 3/4 cups flour, baking powder, and 3/4 teaspoon salt into a medium bowl; set aside.
4 With an electric mixer, cream 1/2 cup butter and cream cheese in a large bowl. Gradually add in 1 1/2 cups sugar, 1/2 cup at a time. Add in the eggs one at a time, beating well after each addition. Add the flour mixture, a third at a time, blending well after each addition. Add the vanilla and lemon zest.
5 Pour the batter into the prepared pan and smooth it with a spoon.
6 To finish the topping, combine 3/4 cup flour, 3/4 cup sugar, cinnamon, and 1/8 teaspoon salt in a large bowl. Mix the butter into the dry ingredients until you have uniform crumbs.
7 Sprinkle half of the crumbs over the batter, then add the apple slices. Top with the apples with the remaining crumbs.
8 Bake the cake on the center rack for 50-60 minutes. When the cake is done, it will pull away from the sides and the top will be golden brown. Cool the cake in the pan on a wire rack.