Preheat oven to 350°F.
Add the butter and brown sugar to the bowl of a stand mixer. Beat on high until light and fluffy. Add the egg, oil and vanilla extract, beating until it resembles frosting.
Stir in the beer (it will curdle).
Sprinkle with flour, salt, cinnamon, nutmeg, and apples. Stir until just combined. Pour into an 8x8 baking dish that has been greased and floured.
Bake for 45-50 minutes or until the top has puffed and springs back when lightly touched.
Add the powdered sugar to the bowl of a stand mixer (or a mixing bowl, and use an electric hand mixer).
Melt the butter in a pot over high heat. Add the brown sugar, cream and vanilla, stir until just combined. Boil over high heat for two minutes.
Pour the caramel over the powdered sugar, beat until well combined. Pour the frosting over the apple bars in an even layer, sprinkle with remaining ¼ teaspoon salt, allow to cool. Cut into squares.