In a medium saucepan, whisk together sugar and cornstarch. Add in milk and butter. Bring to a boil over medium heat, stirring often. This should take about 7-10 minutes. Mixture should thicken nicely- just be sure to continue whisking so that it doesn't stick to the pan.
Once it begins boiling, remove from heat. Add in vanilla and stir to combine. Pour into the graham cracker pie crust. Refrigerate until cold, at least 1 hour.
Just before serving, sprinkle the brown sugar over the top of the pie and broil it in the oven for about 2 minutes. (This step is optional- it tastes great without it but I love the slightly carmelized-sweet taste it adds to the pie.) Top with berries and enjoy!