In a saucepan, whisk together 1/2 cup of the brown sugar, salt and cornstarch until no lumps remain. Add milk and heavy cream and whisk over medium heat until mixture begins to thicken and starts to bubble, about 5 to 7 minutes. Lower heat to medium-low and continue to whisk until thick, about 5 minutes more.

Remove from heat and stir in the remaining 1/4 cup brown sugar, vanilla and butter until smooth.

Pour pudding into a large serving bowl or individual dishes. Cover with plastic wrap, pressing plastic onto the surface of the pudding, and chill until set, about 1-2 hours. Before serving, remove plastic wrap and sprinkle pudding with chocolate chips.