Prepare 9x13 baking dish by greasing with butter. Slice French bread into 2 inch slices and then cube. Place all cubes into prepared dish. Set aside.
In a large bowl, add eggs, pumpkin puree, half and half, milk, sugars, rum, salt, cinnamon, ginger, cloves, and nutmeg. Whisk together to combine.
Pour mixture evenly over the cubed bread. Gently fold to coat all the bread. Press down with the back of the spatula to push bread into the custard. Cover with plastic wrap and refrigerate overnight or for at least 5 hours and no more than 24 hours. We need this time to make sure the bread soaks up all the custard.
Once the pudding has set, preheat oven to 350 degrees. Mix cinnamon and sugar together for the topping. Dust pudding with cinnamon sugar topping. Bake in preheated oven for 40-50 minutes, or until it's no longer jiggling. Remove from oven and let it sit for 10 minutes before serving.
Scoop or slice bread pudding into 12 portions. Top with High Road Fleur de Sel Vanilla Ice Cream and serve immediately.