Preheat the oven to 300°F (150°C). Line an 8x8-inch baking pan with parchment paper, leaving enough parchment extending over the sides to make removing the bars easier.
Prepare the shortbread base. Beat the room-temperature butter with a mixer for about 5 minutes, until light, creamy, and noticeably paler in color.
Add the granulated sugar, vanilla extract, and salt. Mix until well combined.
Add 1 cup of all-purpose flour and mix just until a soft shortbread mixture forms.
Press the shortbread mixture evenly into the bottom of the prepared pan. Bake for 15 minutes.
Meanwhile, prepare the apple filling. Place the thinly sliced apples in a bowl and add 2 tablespoons flour, 2 tablespoons sugar, cinnamon, and nutmeg. Toss until the apple slices are evenly coated.
Make the crumble topping by combining ½ cup flour with the brown sugar. Add the butter and work the ingredients together until a crumbly mixture forms.
Remove the shortbread crust from the oven and increase the oven temperature to 350°F (175°C).
Sprinkle half of the crumble mixture evenly over the partially baked shortbread. Arrange the seasoned apple slices over the crumble in even layers.
Sprinkle the remaining crumble topping over the apples.
Return the pan to the oven and bake the Apple Crisp Shortbread Bars for about 30 minutes, or until the apples are tender and the topping is lightly browned.
Allow the bars to cool completely at room temperature. Refrigerate for at least 2 hours so the layers can firm up.
Lift the dessert from the pan using the parchment paper and cut into 16 squares.
Notes
For a slightly tarter filling, Granny Smith apples work especially well. For more natural sweetness, try Honeycrisp or Pink Lady apples.