Spray a 6-quart slow cooker with a non-stick cooking spray and add bread crumbs.
Add eggs, milk, sugar, butter, cinnamon, nutmeg, and vanilla extract in a medium bowl. Whisk until well combined.
Pour the egg mixture over the bread and gently fold until all the bread is coated.
Cover and cook on high for 1 hour. Reduce the heat to low and cook 3-4 hours.
Just before the bread pudding is done, melt butter in a saucepan over medium heat. Whisk in flour until smooth. While whisking, slowly add in milk, sugar, and vanilla extract.
Pour over bread pudding before serving and enjoy.