Preheat oven to 300°F and line an 8-inch square baking pan with parchment paper.
Make the crust: In a medium bowl, stir together melted butter, sugar, vanilla, salt, and flour until combined. Press mixture evenly into the bottom of the prepared pan. Bake for 20 minutes, then remove from oven.
Make the filling: In a large bowl, toss apples with flour, sugar, cinnamon, and nutmeg until coated. Layer evenly over the baked shortbread crust and press down lightly.
Make the streusel: In another bowl, combine oats, brown sugar, cinnamon, and flour. Cut in cold butter with a pastry cutter or fork until mixture resembles coarse crumbs. Sprinkle evenly over apples.
Increase oven temperature to 350°F. Bake bars for 35–40 minutes, or until the topping is golden brown and apples are tender. Remove from oven and cool completely in the pan.
Make the glaze: Whisk together confectioners’ sugar and milk until smooth. Drizzle over cooled bars before slicing and serving.