Heat the oven to 350°F. Line a 9-by-13-inch metal baking pan with parchment paper and lightly grease any exposed areas.
Whisk the flour, granulated sugar, brown sugar, cinnamon, and salt in a large bowl.
Add the melted butter and vanilla. Stir until thick crumbs form.
Reserve about 2 cups of the mixture for the topping. Press the remaining mixture firmly into the prepared pan.
Bake the crust for 16 to 19 minutes, until set and lightly golden around the edges.
Peel, core, and slice the apples approximately ⅛ to ¼ inch thick.
Melt 3 tablespoons of butter in a large skillet over medium heat.
Add the apples, brown sugar, granulated sugar, lemon juice, cinnamon, nutmeg, and salt. Cook for 6 to 9 minutes, stirring occasionally, until the apples begin to soften.
Whisk the cornstarch and water in a small bowl. Stir it into the apples and cook for 1 to 2 minutes, until the liquid thickens.
Remove the skillet from the heat and stir in the vanilla.
Spread the apple filling and thickened juices evenly over the warm crust.
Crumble the reserved dough over the apples.
Bake for 35 to 43 minutes, until the topping is golden and the filling bubbles around the edges.
Cool completely in the pan for at least 2 hours.
Whisk the powdered sugar, milk, vanilla, and salt until smooth. Drizzle over the cooled bars.
Allow the glaze to set, then lift the bars from the pan and slice.