Place butter in a cast iron skillet over medium high heat.
While the butter melts, stir together next four ingredients in a small bowl.
Add sugar mixture to melted butter and stir until all the butter is absorbed and the mixture is no longer white.
Remove from heat and continuously whisk in half of the half and half. Once the mixture is smooth, return to heat, continue whisking and add remaining half and half. Whisk continuously until pudding thickens. Stir in vanilla extract.
Remove from heat. Serve immediately.
If your preference is cold pudding, remove from heat and keep whisking until the pudding has cooled. Pour into a bowl and cover surface with plastic wrap.