Preheat the oven to 350°F. Grease and flour a 9x9-inch square baking pan.
PREPARE THE BARS:
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon and salt. Set aside.
In a large mixing bowl, use an electric mixer to beat the butter, sugar, eggs and vanilla until fluffy. Stir the flour mixture into the wet mixture, just until combined. Carefully stir in the apples.
Spoon 2/3 of the batter into the prepared pan. Drop the dulce de leche by heaping tablespoons over the batter. Drag a butter knife through the dulce de leche to swirl through the batter. Drop the remaining batter over the dulce de leche. Bake 25 to 30 minutes, or until browned and firm to touch. Let cool completely.
PREPARE THE ICING:
In a small saucepan, heat the butter over medium until it begins to brown. Remove from heat. Add to a bowl with the powdered sugar, vanilla and half/half. Beat on high speed with electric mixer until creamy. Drizzle and spread over bars, and chill until icing is set.
For the cleanest cuts, chill completely and slice into the bars with a sharp, thin knife. Keep refrigerated until ready to serve.
Notes
*You can make your own dulce de leche or purchase it already made. We can usually find it in a can in the Latin section of our local grocery store. The stuff in the can is pretty darn good. You just might want to heat it up for 20 seconds in the microwave before scooping it onto the bars.
*Suggested apple varieties for this recipe: Braeburn, Cox’s Orange Pippin, Granny Smith, Jonathon, Golden Russet