Place evaporated milk, sugar, and vanilla in a large pot, whisk to combine.
Bring to a low simmer over medium heat. Once simmering, set a timer for 10 minutes, stirring occasionally. Keep an eye on the simmering mixture, it may bubble over if the temperature becomes too hot. If boiling, simply reduce the heat until the mixture calms back down into a low simmer.
Remove the pot from the heat and set aside to cool, at room temperature, for another 10 minutes.
Add the chocolate chips and butter, continuously stir until the butter and the chocolate chips have melted and combined. The pudding mixture should be smooth, and shiny.
Pour the pudding mixture into serving bowls or glasses.
Let the pudding cool to room temperature for 15 minutes before placing in the refrigerator, covered. Refrigerate until the pudding has chilled and thickened, about 2-3 hours (or overnight).
Garnish pudding with any of your favorite optional toppings. We love whipped cream and creative cookies.