In a medium saucepan, heat cream and milk over medium-high heat until boiling. Remove from heat and stir in vanilla extract.
In a medium bowl, whisk together sugar and egg yolks until smooth and pale yellow.
Temper the egg yolks by slowly whisking in hot cream mixture a few tablespoons at a time, until about half the cream is incorporated.
Pour egg mixture back into saucepan with remaining cream. Cook over medium heat, stirring constantly with a wooden spoon, until custard thickens enough to coat the back of the spoon, about 5 minutes.
Remove from heat and stir in rum extract if using.
Cut bread pudding into squares and serve warm with vanilla custard sauce drizzled over top.