Preparation

• Heat the oven to 350°F. Cut a piece of parchment into a 9×14-inch rectangle. Line a 9-inch-square baking pan with the parchment (it will extend beyond the pan). Butter the parchment and the unlined sides of the pan.

Make the crust and topping:

• Set aside 2 Tbs. of the flour in a small dish. Whisk together the remaining 1-1/4 cups flour and the salt in a small bowl. In a large mixing bowl, beat the butter with an electric mixer on medium speed until smooth. Add the cream cheese and almond extract and beat on medium until smooth, scraping the bowl as needed, about 1 minute. Add 1/4 cup each of the granulated and brown sugars and beat on medium speed until blended, scraping as needed. Add the flour-salt mixture and 1/3 cup of the almonds and beat on medium low just until the flour is absorbed and the mixture starts to come together in clumps.
• Set aside 2/3 cup of the dough in another bowl and press the remaining dough into the prepared pan in a thin but even layer. Prick it all over with a fork. Bake until the crust is golden, especially around the edges, 18 to 20 minutes. Remove from the oven but keep the oven on.
• While the crust bakes, add the 2 Tbs. reserved flour and the remaining 2 tablespoons each of the granulated and brown sugars to the reserved dough. Mix with your fingertips until well combined and then squeeze the dough together into one clump.

Make the filling:

• In a large mixing bowl, beat the cream cheese with an electric mixer on medium speed until smooth. Add the sugar and beat on medium until combined, scraping the bowl as needed. Add the egg and beat until combined, scraping the bowl as needed. Beat in the lemon zest, lemon juice, and salt.
• Spread the apple slices evenly on the bottom crust and pour the cream cheese filling on top, gently spreading it with a rubber spatula to cover the apples. Crumble the remaining dough on top. The pieces can be fairly large, about the size of a cherry, and the topping needn’t completely cover the filling. Sprinkle with the remaining almonds. Bake until the topping and almonds are light golden brown, 45 to 50 minutes. Let the bars cool in the pan until warm, about 30 minutes. Remove from the pan using the parchment sling and set on a wire rack to cool completely. Transfer the bars, still on the parchment, to a cutting board. Slide a long metal spatula between the bars and parchment to separate them, and then slide the parchment out. Cut into 16 bars.