Add the neufchatel cheese, sugar, cinnamon, nutmeg and vanilla to a mixing bowl and use and electric mixer to blend well.
Add the eggs one at time, mixing well after each addition.
Gradually add the milk and the pumpkin puree.
Spray the bottom of a baking dish with cooking spray and add the bread to the dish.
Slowly pour the liquid mixture over the bread. Use a rubber spatula or the back of a spoon to gently press the bread into the mixture to make sure that it is saturated with the mixture. Let stand for 30 minutes.
Bake at 350° for about 40 minutes or until golden brown.
Top with vanilla sauce and serve while warm.
Vanilla Sauce
Add sugar and cornstarch to a small saucepan.
Add 1 cup of boiling water and stir constantly for about 5 minutes.