Heat cream mixture: Combine sugar and cornstarch in medium saucepan. Stir in half and half. Scrape vanilla bean and add scrapings plus pod to mixture. Cook over medium heat, stirring frequently until mixture is thick and bubbly and starts to stick to the bottom. This should take about 5-10 minutes.
Temper egg yolks: Add egg yolks to medium-sized bowl. Slowly add one ladle of hot cream mixture to egg yolks while whisking rapidly. Continue to ladle hot mixture into egg yolks until at least one cup of hot mixture has been added. Then, pour warm tempered egg yolk mixture into hot half and half mixture on the stove, whisking constantly.
Cook pudding: Allow mixture to come to a gentle boil, then reduce heat to low. Continue to stir and allow to cook until thickened, about 2-5 more minutes. Remove from heat and stir in butter and salt.
Serve: Transfer pudding to a glass container and cover with plastic wrap. To avoid having a skin form, place plastic wrap right on top of pudding surface. Vanilla bean pod can remain in pudding mixture until ready to serve. Serve warm or cold!
Makes about 4 cups. Serving size based on 1/2 cup.