Heat the oven to 350°F. Grease a 9 x 13-inch baking dish.
Arrange the bread cubes evenly in the baking dish.
In a large bowl, whisk together the pumpkin puree, eggs, brown sugar, granulated sugar, melted butter, vanilla, cinnamon, ginger, nutmeg, cloves, and salt.
Slowly whisk in the whole milk and heavy cream until the custard is smooth.
Pour the custard evenly over the bread. Gently press the bread into the liquid.
Let the mixture soak for 20 to 30 minutes, pressing the bread down once or twice.
Sprinkle with coarse sugar and pecans, if using.
Bake uncovered for 45 to 55 minutes. The edges should be set, the top should be golden, and the center should have only a slight wobble.
Place the dish on a cooling rack and let it rest for at least 15 minutes.
To prepare the sauce, melt the butter in a small saucepan over medium-low heat.
Stir in the maple syrup, heavy cream, and salt. Cook for 3 to 5 minutes, stirring regularly.
Remove the sauce from the heat and stir in the vanilla.
Spoon the warm bread pudding into bowls and drizzle with maple vanilla sauce.