Peel and slice apples into thin slices. In a pan over medium heat, add the apple slices with cinnamon and brown sugar. Cook the apples, stirring occasionally, but do not let them become soft. Set the apples aside.
Preheat oven to 300°F. In a pan over medium heat, add sugar and let it begin to caramelize before stirring until smooth.
Place the prepared apple slices evenly in the baking pan. Pour the caramelized sugar over the apples, tilting the pan to spread evenly, then place the pan in the freezer while you make the flan mixture.
In a blender, lightly pulse the eggs, yolks, and dulce de leche without creating too many bubbles. In a large bowl, mix heavy cream, evaporated milk, condensed milk, vanilla, and the egg mixture, being careful not to create air pockets. Strain 3 times until smooth.
Remove the caramelized pan with apples from the freezer and place it in a large baking dish. Pour the flan mixture into the pan. Add hot water to the baking dish to come halfway up the sides of the flan pan.
Bake for 1 hour and 30 minutes. Remove from oven and water bath, and let the flan rest at room temperature for 1 hour. Cover and refrigerate overnight.
The next day, run a knife along the edges of the pan. Place a plate over the pan, flip, and gently shake to release the flan. Slice and serve. Buen provecho!