In a medium-size bowl, whisk together the sugar, flour, and salt.
Whisk in half a cup of heavy whipping cream and continue whisking until no lumps remain.
Whisk in remaining heavy whipping cream and vanilla extract.
Transfer contents to a medium-size saucepan and cook over medium-low heat, whisking continuously.
After about 5 minutes, when the mixture is warm but not boiling, pour 1/4 cup of the cream mixture into the lightly beaten eggs and whisk quickly to temper the pudding.
Immediately pour the eggs into the saucepan and continue whisking over medium-low heat.
After several minutes, the pudding will start to thicken and bubble. Remove from heat.
Cover the top of the pudding with plastic wrap making sure that the entire surface of the pudding is in contact with the plastic wrap. Poke 5 holes into the plastic wrap using a toothpick.
Let cool for 30 minutes at room temperature before transferring to the refrigerator. Chill for at least 2 hours.