In a medium non-reactive saucepan combine the sugar, cornstarch, half and half, lemon zest, and lemon juice over medium-high heat, stirring often, until mixture starts to bubble.
Once simmering, turn heat down to medium and cook for an additional 1 minute, whisking constantly. NOTE: set a timer for 1 minute and DO NOT OVER COOK. Mixture should be thickened, creamy, and reduced in size (by about a 1/3). Remove saucepan from heat.
‘Temper’ egg yolks by adding a spoonful of hot lemon mixture in to the egg yolks. Stirring constantly to incorporate. Repeat with one additional spoonful, stirring constantly; add the tempered eggs into lemon mixture.
Return pan to stovetop on medium heat and cook for an additional 90 seconds, stirring constantly.
Take pan off heat and stir in butter and vanilla.
Once the butter is melted, pour lemon mixture into prepared graham cracker crust.
Cool pie in the refrigerator for a minimum of 2 hours
Once cooled, garnish with whipped cream, lemon slices, lemon zest, and/or fresh mint.