In a blender, combine the evaporated milk, skim milk and avocado. Puree until smooth.

Add the eggs, cocoa powder, maple syrup and dark rum. Puree until combined.

Place the bread cubes in a large bowl and pour the avocado mixture over the bread. Stir to completely coat the bread.

Lightly coat an 8- by 8-inch square baking pan with cooking spray. Transfer the bread mixture to the baking pan, cover and refrigerate for 30 minutes to 4 hours.

Preheat the oven to 350 degrees F.

Place the baking pan in a 9- by 13-inch baking dish. Pour hot water into the large baking dish until it reaches about 1-inch up the side of the smaller baking pan.

Bake until a sharp knife inserted in the center of the bread pudding comes out clean, 35 to 40 minutes.

Cut into 9 pieces. Serve each piece with 1 tablespoon plus 2 teaspoons of the sauce.

In a small saucepan, combine the maple syrup, rum and butter. Bring to a boil of medium-high heat, whisking frequently.

Add 3 tablespoons of half-and-half, reduce to a simmer and cook, whisking frequently, until the sauce starts to thicken, 7 to 8 minutes.

Remove from the heat and whisk in the remaining tablespoon of half-and-half and the salt.