In a large mixing bowl, whisk the pumpkin puree, eggs, milk, granulated sugar, cinnamon, nutmeg, and vanilla until smooth.
Add the bread cubes to the bowl and stir gently until all pieces are coated. Let the mixture rest for 5 minutes so the bread absorbs some liquid.
Pour everything into the slow cooker and spread it into an even layer.
Cover and cook on low for 3 to 4 hours, until the center is set and a knife inserted comes out mostly clean.
When the pudding is nearly done, make the sauce. Melt the butter in a small saucepan over medium heat.
Stir in the brown sugar, bourbon, and heavy cream. Simmer for 3 to 4 minutes, stirring often, until the sauce thickens slightly.
Turn off the slow cooker and spoon the warm bread pudding into bowls. Drizzle each serving with bourbon sauce.