Meanwhile, whisk together the sugar, cornstarch, and eggs in a medium heatproof bowl. Once the milk is at a simmer, ladle approximately 1/2 cup of milk into the eggs and whisk to combine. Repeat with two more 1/2 cup additions, then pour the warmed eggs into the pot. Cook over medium heat, whisking constantly, until the pudding turns thick and lumpy, about 3 minutes. Once the pudding begins bubbling, continue cooking and whisking for 2 minutes more.