In a heavy-bottomed saucepan over medium heat, heat milk and vanilla bean and seeds for 5 minutes. Remove from heat, cover, and let sit for 10 minutes. Strain mixture into a small bowl, discarding bean.
In same saucepan, mix together sugar, cornstarch and salt. Gradually stir in heavy cream until completely smooth. Whisk in milk mixture.
Cook over medium heat, stirring constantly, until pudding begins to thicken, about 15 minutes. Reduce heat; bring to a gentle simmer, about 15 minutes. Cook 1 minute more.
Remove pan from heat and stir in vanilla extract.
Pour pudding into medium-size bowl or individual ramekins, covering the surface directly with plastic wrap.
Refrigerate for 2 hours or overnight before serving.