Melt the butter in a medium saucepan over medium heat. Add the golden erythritol and stir constantly for 2 to 3 minutes until the mixture deepens in color and smells rich and caramel-like. Watch carefully so it does not burn.
Slowly pour in the heavy cream while whisking constantly. The mixture will bubble vigorously when the cold cream hits the hot butter, so add it in a thin stream. Continue whisking until smooth and heated through.
In a separate bowl, whisk the egg yolks until smooth. Slowly ladle about 1/3 cup of the hot cream mixture into the yolks while whisking quickly. This tempers the eggs so they don't scramble.
Pour the tempered yolk mixture back into the saucepan, whisking constantly. Cook over medium-low heat, stirring continuously, for 5 to 6 minutes until the pudding thickens enough to coat the back of a spoon. Sprinkle in the xanthan gum while whisking to prevent any clumps from forming.
Remove from heat and stir in the vanilla extract, butter extract, and salt. Strain the pudding through a fine mesh sieve into a bowl to catch any lumps.
Divide the pudding among 4 serving cups. Press plastic wrap directly onto the surface of each pudding to prevent a skin from forming. Refrigerate for at least 3 hours until cold and set. Serve topped with a swirl of whipped cream.
