In a medium saucepan, combine milk and ⅛ cup sugar. Place over medium-low heat until mixture comes to a simmer.
In a medium bowl, whisk together egg yolks, cornstarch, and remaining sugar.
Temper eggs: while whisking constantly, slowly pour ⅓ of the hot milk mixture into the egg-yolk mixture, until it has been incorporated. Pour mixture back into the saucepan, and cook over medium-high heat, whisking constantly, for roughly 3-4 minutes, until it thickens a lot.
Add the ube extract. Stir until color is uniform throughout.
Remove from the heat and whisk in the butter. Pass the mixture through a sieve to remove any lumps.
