In a medium saucepan, whisk together the coffee creamer, salt, granulated sugar, and cornstarch until combined and fully incorporated. Turn the heat to medium-high and cook, stirring occasionally, until mixture has thickened, about 5-7 minutes. Make sure the mixture doesn't scorch! Remove from the heat.
Whisk the egg yolks until lightly beaten. Temper the eggs by adding a Tablespoon or two of the hot sugar mixture to the eggs, whisking constantly. Temper again with another Tablespoon if needed. Pour the tempered egg yolks into the sugar mixture along with the vanilla extract and butter, stirring until melted and combined.
Spoon the pudding mixture into individual bowls or cups, or pour into a large bowl. Cover the pudding with plastic wrap by gently pressing the plastic wrap onto the surface of the pudding - this helps prevent a film from forming on the pudding. Refrigerate until chilled, about 1-2 hours.
Just before serving, garnish with fresh whipped cream and berries, if desired.