In a small thick-bottomed saucepan mix together the water and the granulated sugar until well blended. Bring to a boil over medium-low heat and continue boiling until the mixture turns a light caramel color, only stirring once every four minutes. This took me about eight minutes, but the speed will depend upon the heat of your stovetop.

Remove the pan from the heat and quickly stir in the heavy cream, brown sugar, and butter until incorporated. Be careful as the mixture will spit and hiss a bit. If the sugar begins to clump up when you’re stirring do not fret, just stir as best as you can for about 30 seconds and then put the pot back on the heat and bring it back to a boil again over medium-low heat. Once it is boiling again stir until the sugar chunk dissolves and the mixture is smooth. Once it smoothes out, stir it every two minutes and allow the mixture to simmer for 5 minutes to thicken slightly. Remove from the stovetop and stir in the salt. Allow to cool to room temperature.

Preheat the oven to 350 degrees Fahrenheit. Place an 8-inch cake pan two thirds full of water on the lowest rack of the oven. This will fill the oven with steam as it simmers and help keep the bread pudding moist. Generously grease a 10-inch in diameter and 3-inch deep circular baking pan with unsalted butter.

In a large bowl, whisk together the eggs, egg yolks, milk, cream, maple, honey, vanilla, cinnamon, allspice, and salt until completely smooth.

In a separate large bowl, toss together the bread cubes and chopped apple. Pour the egg mixture over the bread mixture and toss gently with your hands to coat. Allow the mixture to soak for 15 minutes.

In a medium bowl, toss together the apple slices with the olive oil and 2 tablespoons of the sugar. Set aside.

Pour the bread mixture into the baking pan, pressing down on the bread pudding in the pan to compress the bread cubes to allow them all to fit in the pan. Arrange the apple slices in a spiral-shaped pattern over the bread pudding. Dot with the butter and sprinkle with the remaining tablespoon sugar. Place the pan on a rack just above the water-filled cake pan and bake until the bread pudding pulls away from the sides of the pan and looks golden on top, about 50 minutes. Remove the bread pudding from the oven and allow to cool for 20 minutes before drizzling with the caramel sauce and serving.